Ejercicios campo eléctrico distribuciones continuas.
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This document contains 12 practice problems about electric fields. The problems cover topics like calculating the electric field from uniformly charged rods, rings, disks, and semicircular shapes at various distances from the charge distributions. They also include finding the electric field from non-uniform charge distributions along axes and between oppositely charged semicircular shapes. Solutions involve using the electric field equations and considering the geometry of the charge distributions.
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1. The magnetic field created by a current-carrying wire can be calculated by considering the magnetic field dB created by a small segment of wire dl, and then integrating over the full length of the wire.
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Physics 226 Fall 2013 Problem Set #1 NOTE Sh.docx
Physics 226
Fall 2013
Problem Set #1
NOTE: Show ALL work and ALL answers on a piece of separate loose leaf paper, not on this sheet.
Due on Thursday, August 29th
1) Skid and Mitch are pushing on a sofa in opposite
directions with forces of 530 N and 370 N respectively.
The mass of the sofa is 48 kg. The sofa is initially at rest
before it accelerates. There is no friction acting on the
sofa. (a) Calculate the acceleration of the sofa. (b) What
velocity does the sofa have after it moves 2.5 m? (c) How
long does it take to travel 2.5 m?
2) You have three force
vectors acting on a
mass at the origin.
Use the component
method we covered
in lecture to find
the magnitude and
direction of the re-
sultant force acting
on the mass.
3) You have three force
vectors acting on a
mass at the origin.
Use the component
method we covered
in lecture to find
the magnitude and
direction of the re-
sultant force acting on
the mass.
4) A bowling ball rolls off of a table that is 1.5 m tall. The
ball lands 2.5 m from the base of the table. At what speed
did the ball leave the table?
5) Skid throws his guitar up
into the air with a velocity
of 45 m/s. Calculate the
maximum height that the
guitar reaches from the point
at which Skid let’s go of the
guitar. Use energy methods.
6)
A beam of mass 12 kg and length 2 m is attached to a
hinge on the left. A box of 80 N is hung from the beam
50 cm from the left end. You hold the beam horizontally
with your obviously powerful index finger. With what
force do you push up on the beam?
7) The tennis ball of mass 57 g which
you have hung in your garage that
lets you know where to stop your
car so you don’t crush your garbage
cans is entertaining you by swinging
in a vertical circle of radius 75 cm.
At the bottom of its swing it has a
speed of 4 m/s. What is the tension
in the string at this point?
Mitch Sofa Skid
y
F2 = 90 N
F1 = 40 N 35
8) Derivatives:
a) Given: Lx2Lx4y 22 , find
dx
dy
.
b) Given:
Lx2
Lx2lny , find
dx
dy
.
9) Integrals:
a) Given:
o
o
45
45
d
r
cosk
, evaluate.
b) Given:
R
0 2322
dr
xr
kx , evaluate.
ANSWERS:
1) a) 3.33 m/s2
b) 4.08 m/s
c) 1.23 s
2) 48.0 N, 61.0º N of W
3) 27.4 N, 16.1º S of E
4) 4.5s m/s
5) 103.3 m
6) 78.8 N
7) 1.78N
8) a) 24x2 + 8xL – 4L
b) 22 x4L
L4
9) a)
r
k2
b)
22 xR
x1k2
45 x
F3 = 60 N
y
F2 = 65 N
F1 = 45 N 60
50 x
70
F3 = 60 N
Guitar
Skid
Physics 226
Fall 2013
Problem Set #2
1) A plastic rod has a charge of –2.0 C. How many
electrons must be removed so that the charge on the rod
becomes +3.0C?
–
+
+
+
2)
Three identical metal spheres, A, B, and C initially have
net charges as shown. The “q” .
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- 1. TALLER DE REPASO DE CAMPO ELÉCTRICO FÍSICA ELÉCTRICA 1. A lo largo del eje x existe una línea de carga continua que se extiende desde 𝑥 = 𝑥0 hasta el infinito positivo. La línea tiene una densidad de carga lineal uniforme 𝜆0. ¿Cuál es la magnitud y la dirección del campo eléctrico en el origen? 2. Una varilla de 14.0 cm de largo tiene una carga uniforme y su carga total es de 22 μC. Determine la magnitud y dirección del campo eléctrico a lo largo del eje de la varilla en un punto a 36 cm de su centro. 3. Un anillo con un radio de 10 cm con carga uniforme tiene una carga total igual a 75 μC. Determine el campo eléctrico sobre el eje del anillo a las siguientes distancias del centro del mismo: a) 1 cm, b) 5 cm, c) 30 cm y d) 100 cm. 4. Un disco con carga uniforme con un radio de 35 cm tiene una densidad de carga de 7.97,9 ∗ 103 𝐶 𝑚2 . Calcule el campo eléctrico en el eje del disco a a) 5 cm, b) 10 cm, c) 50 cm y d) 200 cm del centro del mismo. 5. Una barra aisladora uniformemente cargada, de 14.0 cm de longitud, se dobla en la forma de un semicírculo. La barra tiene una carga total de 7.50 μC. Encuentre la magnitud y dirección del campo eléctrico en el centro del semicírculo. 6. Una varilla delgada de longitud l con carga uniforme por unidad de longitud λ yace a lo largo del eje x. Encuentre que el campo eléctrico en P, a una distancia y de la varilla sobre su parte central. 7. Una barra delgada tiene sus extremos en x = ±100 cm. A lo largo de la barra hay una carga Q distribuida uniformemente. a) ¿Cuál es el campo eléctrico que está muy cerca del punto medio de la barra? b) ¿Cuál es el campo eléctrico que está a unos cuantos centímetros (perpendicularmente) del punto medio de la barra? c) ¿Cuál es el campo eléctrico que está muy lejos (perpendicularmente) del punto medio de la barra? 8. Una carga por unidad de longitud +λ está distribuida uniformemente a lo largo del eje y positivo desde y = 0 hasta y = +a. Una carga por unidad de longitud –λ está distribuida uniformemente a lo largo del eje y negativo desde y = 0 hasta y = –a. Escriba una expresión para el campo eléctrico (magnitud y dirección) en un punto sobre el eje x a una distancia x del origen. 9. Una varilla delgada de vidrio se dobla en forma de semicírculo de radio R. Una carga +Q está distribuida uniformemente a lo largo de la mitad superior, y una carga –Q está distribuida uniformemente a lo largo de la mitad inferior. Encuentre la magnitud y dirección del campo eléctrico E en el centro del semicírculo. 10. Dos barras aislantes cargadas uniformemente se doblan en forma semicircular con radio r = 10 cm. Si se colocan de modo que formen un círculo, pero sin tocarse, y tengan cargas opuestas de +10 μC y –10 μC, encuentre la magnitud y dirección del campo eléctrico en el centro de la configuración circular.
- 2. 11. Una barra de longitud L cargada uniformemente con carga total Q se encuentra a lo largo del eje y, desde y = 0 hasta y = L. Encuentre una expresión para el campo eléctrico en el punto (d, 0) (es decir, el punto en x = d sobre el eje x). 12. Una rondana delgada y plana es un disco con diámetro exterior de 10 cm y un hueco en el centro con diámetro de 4 cm, y tiene una distribución de carga uniforme y una carga total de 7 nC. ¿Cuál es el campo eléctrico sobre el eje de la rondana a una distancia de 30 cm desde su centro? BIBLIOGRAFÍA • Bauer Wolfgang, Westfall Gary. Física para ingeniería y ciencias con física moderna. Vol. 2. Edit. McGrawHill. Segunda edición. México. • Raymond A. Serway y John W. Jewett, Jr. Física para ciencias e ingeniería. Volumen 1. Séptima edición. •