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Learning Objectives
Define electric charge, and describe how the two types of charge interact.
Desribe three common situations that generate static electricity. State the law of conservation of charge.
Describe three methods for charging an object.
State Coulomb’s law
Describe an electric field diagram of a positive point charge; of a negative point charge with twice the magnitude of positive charge
Draw the electric field lines between two points of the same charge; between two points of opposite charge.
Thank you So much
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
2. A coulomb is the same as:
A. an ampere/second
B. half an ampere·second2
C. an ampere/meter2
D. an ampere·second
E. a newton·meter2
3. A kiloampere·hour is a unit of:
A. current
B. charge per time
C. power
D. charge
E. energy
4. A wire carries a steady current of 2 A. The charge
that passes a cross section in 2 s is:
A. 3.2 × 10-19 C
B. 6.4 × 10-19 C
C. 1C
D. 2C
E. 4C
5. A wire contains a steady current of 2 A. The
number of electrons that pass a cross section in
2 s is:
A. 2
B. 4
C. 6.3 × 1018
D. 1.3 × 1019
E. 2.5 × 1019
6. The charge on a glass rod that has been rubbed
with silk is called positive:
A. by arbitrary convention
B. so that the proton charge will be positive
C. to conform to the conventions adopted for G
and m in Newton’s law of gravitation
D. because like charges repel
E. because glass is an insulator
7. To make an uncharged object have a positive
charge:
A. remove some neutrons
B. add some neutrons
C. add some electrons
D. remove some electrons
E. heat it to cause a change of phase
8. When a hard rubber rod is given a negative
charge by rubbing it with wool:
A. positive charges are transferred from rod to
wool
B. negative charges are transferred from rod to
wool
C. positive charges are transferred from wool to
rod
D. negative charges are transferred from wool to
rod
E. negative charges are created and stored on the
rod
9. An electrical insulator is a material:
A. containing no electrons
B. through which electrons do not flow easily
C. that has more electrons than protons on its
surface
D. cannot be a pure chemical element
E. must be a crystal
10. The diagram shows two pairs of heavily charged
plastic cubes. Cubes 1 and 2 attract each other and
cubes 1 and 3 repel each other.
Which of the following illustrates the forces of
cube 2 on cube 3 and cube 3 on cube 2?
11. The diagram shows a pair of heavily charged plastic
cubes that attract each other.
Cube 3 is a conductor and is uncharged. Which of
the following illustrates the forces between cubes 1
and 3 and between cubes 2 and 3?
12. Two uncharged metal spheres, L and M, are in contact.
A positively charged rod is brought close to L, but not
touching it, as shown. The two spheres are slightly
separated and the rod is then withdrawn. As a result:
A. both spheres are neutral
B. both spheres are positive
C. both spheres are negative
D. L is negative and M is positive
E. L is positive and M is negative
ans: D
13. A neutral metal ball is suspended by a string. A
positively charged insulating rod is placed
near the ball, which is observed to be attracted to
the rod. This is because:
A. the ball becomes positively charged by induction
B. the ball becomes negatively charged by
induction
C. the number of electrons in the ball is more than
the number in the rod
D. the string is not a perfect insulator
E. there is a rearrangement of the electrons in the
ball
14. Two small charged objects attract each other with a
force F when separated by a distance d. If the
charge on each object is reduced to one-fourth of its
original value and the distance between them is
reduced to d/2 the force becomes:
A. F/16
B. F/8
C. F/4
D. F/2
E. F
15. Two identical conducting spheres A and B carry
equal charge. They are separated by a distance
much larger than their diameters. A third identical
conducting sphere C is uncharged. Sphere
C is first touched to A, then to B, and finally
removed. As a result, the electrostatic force
between A and B, which was originally F, becomes:
A. F/2
B. F/4
C. 3F/8
D. F/16
E. 0
16. Two particles, X and Y, are 4m apart. X has a charge
of 2Q and Y has a charge of Q. The
force of X on Y:
A. has twice the magnitude of the force of Y on X
B. has half the magnitude of the force of Y on X
C. has four times the magnitude of the force of Y
on X
D. has one-fourth the magnitude of the force of Y
on X
E. has the same magnitude as the force of Y on X
17. A 5.0-C charge is 10m from a −2.0-C charge. The
electrostatic force on the positive charge is:
A. 9.0 × 108 N toward the negative charge
B. 9.0 × 108 N away from the negative charge
C. 9.0 × 109 N toward the negative charge
D. 9.0 × 109 N away from the negative charge
E. none of these
18. Two identical charges, 2.0m apart, exert forces of
magnitude 4.0N on each other. The value of either
charge is:
A. 1.8 × 10-9 C
B. 2.1 × 10-5 C
C. 4.2 × 10-5 C
D. 1.9 × 105 C
E. 3.8 × 105 C
19. Two electrons (e1 and e2) and a proton (p) lie on a
straight line, as shown. The directions of
the force of e2 on e1, the force of p on e1, and the
total force on e1, respectively, are:
A. →, ←, →
B. ←, →, →
C. →, ←, ←
D. ←, →, ←
E. ←, ←, ←
20. Particles 1, with charge q1, and 2, with charge q2, are
on the x axis, with particle 1 at x = a
and particle 2 at x = −2a. For the net force on a third
charged particle, at the origin, to be
zero, q 1 and q2 must be related by q2 =:
A. 2q1
B. 4q1
C. −2q1
D. −4q1
E. −q1/4
21. Two particles A and B have identical charge Q. For a
net force of zero to be exerted on a third
charged particle it must be placed:
A. midway between A and B
B. on the perpendicular bisector of the line joining
A and B but away from the line
C. on the line joining A and B, not between the
particles
D. on the line joining A and B, closer to one of them
than the other
E. at none of these places (there is no place)
22. A particle with charge 2-μC is placed at the origin,
an identical particle, with the same charge,
is placed 2m from the origin on the x axis, and a
third identical particle, with the same charge,
is placed 2m from the origin on the y axis. The
magnitude of the force on the particle at the
origin is:
A. 9.0 × 10-3 N
B. 6.4 × 10-3 N
C. 1.3 × 10-2 N
D. 1.8 × 10-2 N
E. 3.6 × 10-2 N
23. Two particles, each with charge Q, and a third
particle, with charge q, are placed at the vertices
of an equilateral triangle as shown. The total force on
the particle with charge q is:
A. parallel to the left side of the triangle
B. parallel to the right side of the triangle
C. parallel to the bottom side of the triangle
D. perpendicular to the bottom side of the triangle
E. perpendicular to the left side of the triangle
25. An electric field is most directly related to:
A. the momentum of a test charge
B. the kinetic energy of a test charge
C. the potential energy of a test charge
D. the force acting on a test charge
E. the charge carried by a test charge
26. As used in the definition of electric field, a “test
charge”:
A. has zero charge
B. has charge of magnitude 1C
C. has charge of magnitude 1.6 × 10-19 C
D. must be an electron
E. none of the above
27. Experimenter A uses a test charge q0 and
experimenter B uses a test charge −2q0 to measure
an electric field produced by stationary charges. A
finds a field that is:
A. the same in both magnitude and direction as
the field found by B
B. greater in magnitude than the field found by B
C. less in magnitude than the field found by B
D. opposite in direction to the field found by B
E. either greater or less than the field found by B,
depending on the accelerations of the test
charges
28. The units of the electric field are:
A. J/(C·m)
B. J/C
C. J·C
D. J/m
E. none of these
29. Two thin spherical shells, one with radius R and the
other with radius 2R, surround an isolated
charged point particle. The ratio of the number of
field lines through the larger sphere to the
number through the smaller is:
A. 1
B. 2
C. 4
D. 1/2
E. 1/4
30. Choose the correct statement concerning electric
field lines:
A. field lines may cross
B. field lines are close together where the field is
large
C. field lines point away from a negatively
charged particle
D. a charged point particle released from rest
moves along a field line
E. none of these are correct
31. The diagram shows the electric field lines due to two
charged parallel metal plates. We conclude that:
A. the upper plate is positive and the lower plate
is negative
B. a proton at X would experience the same force
if it were placed at Y
C. a proton at X experiences a greater force than
if it were placed at Z
D. a proton at X experiences less force than if it
were placed at Z
E. an electron at X could have its weight balanced
by the electrical force
32. Let k denote 1/4πε0. The magnitude of the electric
field at a distance r from an isolated point
particle with charge q is:
A. kq/r
B. kr/q
C. kq/r3
D. kq/r2
E. kq2/r2
33. The diagram shows the electric field lines in a region
of space containing two small charged spheres (Y
and Z). Then:
A. Y is negative and Z is positive
B. the magnitude of the electric field is the same
everywhere
C. the electric field is strongest midway between Y
and Z
D. the electric field is not zero anywhere (except
infinitely far from the spheres)
E. Y and Z must have the same sign
34. The electric field at a distance of 10 cm from an
isolated point particle with a charge of 2×10-9 C is:
A. 1.8N/C
B. 180N/C
C. 18N/C
D. 1800N/C
E. none of these
35. An isolated charged point particle produces an
electric field with magnitude E at a point 2m away.
At a point 1m from the particle the magnitude of
the field is:
A. E
B. 2E
C. 4E
D. E/2
E. E/4
36. Two protons (p1 and p2) are on the x axis, as shown
below. The directions of the electric field
at points 1, 2, and 3, respectively, are:
37. Two point particles, with a charges of q1 and q2,
are placed a distance r apart. The electric field is
zero at a point P between the particles on the line
segment connecting them. We conclude that:
A. q1 and q2 must have the same magnitude and
sign
B. P must be midway between the particles
C. q1 and q2 must have the same sign but may
have different magnitudes
D. q1 and q2 must have equal magnitudes and
opposite signs
E. q1 and q2 must have opposite signs and may
have different magnitudes
38. The diagrams below depict four different charge
distributions. The charge particles are all the
same distance from the origin. The electric field at
the origin:
A. is greatest for situation 1
B. is greatest for situation 3
C. is zero for situation 4
D. is downward for situation 1
E. is downward for situation 3
39. The diagram shows a particle with positive charge Q
and a particle with negative charge −Q. The electric
field at point P on the perpendicular bisector of the
line joining them is:
A. ↑
B. ↓
C. →
D. ← E. zero
40. Two point particles, one with charge +8 × 10−9 C and
the other with charge −2 × 10−9 C, are
separated by 4m. The electric field in N/C midway
between them is:
A. 9 × 109
B. 13, 500
C. 135, 000
D. 36 × 10−9
E. 22.5
41. Positive charge Q is uniformly distributed on a
semicircular rod. What is the direction of the
electric field at point P, the center of the semicircle?
42. The electric field due to a uniform distribution of
charge on a spherical shell is zero:
A. everywhere
B. nowhere
C. only at the center of the shell
D. only inside the shell
E. only outside the shell
43. The magnitude of the force of a 400-N/C electric
field on a 0.02-C point charge is:
A. 8.0N
B. 8 × 10−5 N
C. 8 × 10−3 N
D. 0.08N
E. 2 × 1011 N
44. A 200-N/C electric field is in the positive x
direction. The force on an electron in this field is:
A. 200N in the positive x direction
B. 200N in the negative x direction
C. 3.2 × 10−17 N in the positive x direction
D. 3.2 × 10−17 N in the negative x direction
E. 0
45. Two charged particles are arranged as shown. In
which region could a third particle, with
charge +1 C, be placed so that the net electrostatic
force on it is zero?
A. I only
B. I and II only
C. lII only
D. I and III only
E. II only
47. A total charge of 6.3×10−8 C is distributed uniformly
throughout a 2.7-cm radius sphere. The volume
charge density is:
A. 3.7 × 10−7 C/m3
B. 6.9 × 10−6 C/m3
C. 6.9 × 10−6 C/m2
D. 2.5 × 10−4 C/m3
E. 7.6 × 10−4 C/m3
48. A spherical shell has an inner radius of 3.7 cm and
an outer radius of 4.5 cm. If charge is distributed
uniformly throughout the shell with a volume
density of 6.1×10−4 C/m3 the total charge is:
A. 1.0 × 10−7 C
B. 1.3 × 10−7 C
C. 2.0 × 10−7 C
D. 2.3 × 10−7 C
E. 4.0 × 10−7 C
49. The flux of the electric field (24N/C)ˆi + (30N/C)ˆj +
(16N/C)ˆk through a 2.0m2 portion of the yz plane
is:
A. 32N · m2 /C
B. 34N · m2 /C
C. 42N · m2 /C
D. 48N · m2 /C
E. 60N · m2 /C
50.
51. A charged point particle is placed at the center of a
spherical Gaussian surface. The electric
flux ΦE is changed if:
A. the sphere is replaced by a cube of the same
volume
B. the sphere is replaced by a cube of one-tenth
the volume
C. the point charge is moved off center (but still
inside the original sphere)
D. the point charge is moved to just outside the
sphere
E. a second point charge is placed just outside the
sphere
52. Choose the INCORRECT statement:
A. Gauss’ law can be derived from Coulomb’s law
B. Gauss’ law states that the net number of lines
crossing any closed surface in an outward
direction is proportional to the net charge
enclosed within the surface
C. Coulomb’s law can be derived from Gauss’ law
and symmetry
D. Gauss’ law applies to a closed surface of any
shape
E. According to Gauss’ law, if a closed surface
encloses no charge, then the electric field must
vanish everywhere on the surface
53. The outer surface of the cardboard center of a paper
towel roll:
A. is a possible Gaussian surface
B. cannot be a Gaussian surface because it encloses
no charge
C. cannot be a Gaussian surface since it is an
insulator
D. cannot be a Gaussian surface because it is not a
closed surface
E. none of the above
ans: D
54. A physics instructor in an anteroom charges an
electrostatic generator to 25 μC, then carries
it into the lecture hall. The net electric flux in N ·
m2/C through the lecture hall walls is:
A. 0
B. 25 × 10−6
C. 2.2 × 105
D. 2.8 × 106
E. can not tell unless the lecture hall dimensions
are given
55. A solid insulating sphere of radius R contains positive
charge that is distributed with a volume charge density
that does not depend on angle but does increase with
distance from the sphere center. Which of the graphs
below might give the magnitude E of the electric field
as a function of the distance r from the center of the
sphere?
ans: D
56.
57. Which of the following graphs represents the
magnitude of the electric field as a function of the
distance from the center of a solid charged conducting
sphere of radius R?
ans: E