Physics

1. Magnetic Field
Due To Toroid

2. Magnetic Field Due To Toroid
Toroid is a solenoid
bent in ring shape
𝐑𝟏
𝐑𝟐
In the empty space surrounded by
Toroid (r < R1)
ර 𝐁 ∙ 𝐝Ԧ
l = 𝛍𝐨𝐈𝐞𝐧𝐜
𝐈𝐞𝐧𝐜 = 0
𝐁 = 0
𝒓
𝐀
POINT - A

3. Magnetic Field Due To Toroid
Outside the Toroid (r > R2)
ර 𝐁 ∙ 𝐝Ԧ
l = 𝛍𝐨𝐈𝐞𝐧𝐜
𝐈𝐞𝐧𝐜 = NI – NI = 0
𝐁 = 0
𝐑𝟏
𝐑𝟐
𝒓
POINT - B
𝐁

4. Magnetic Field Due To Toroid
Inside the Toroid (R1 ≤ r ≤ R2)
ර 𝐁 ∙ 𝐝Ԧ
l = 𝛍𝐨𝐈𝐞𝐧𝐜
𝐑𝟏
𝐑𝟐
𝒓
POINT - C
𝐂
ර 𝐁𝐝l = 𝛍𝐨(𝐍𝐈)
𝐁 𝟐𝛑𝐫 = 𝛍𝐨(𝐍𝐈)
𝐁 = 𝛍𝐨𝐧𝐈
𝐁 = 𝛍𝐨
𝐍
𝟐𝛑𝐫 I

5. Magnetic Field Due To Toroid
Inside the Toroid (R1 ≤ r ≤ R2)
𝐑𝟏
𝐑𝟐
𝒓
POINT - C
𝐂
If r is not given, then for magnetic field
inside the toroid
𝐧 =
𝐍
𝟐𝛑𝐫𝐦
𝐫𝐦 =
𝐑𝟏 + 𝐑𝟐
𝟐
Mean
Radius
𝐁 = 𝛍𝐨𝐧𝐈

6. A toroid has a core of inner radius 24 cm and outer radius 26 cm with total
number of turns N = 1000. It current in wire is 10 A, find out the magnetic
field-
1. Outside the toroid
2. Inside the toroid core
3. In the empty space surrounded by toroid
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

7. 𝐑𝟏
𝐑𝟐
Magnetic field of toroid is non uniform because at each point direction
of magnetic field is not same.
Among many other uses like
solenoid, it is used to generate
concentric circular magnetic field
lines in laboratories.

8. Motion of Charge
Particle in
External Magnetic
Field

9. v
B
θ
Motion of Charge Particle in External Magnetic Field
It experiences a force, given by-
Ԧ
𝐅 = 𝐪(𝐯 × 𝐁)
F= qvB sinθ
When a charged particle moves in an external magnetic field B with a
non-zero velocity v.

10. If v = 0, then F = qvB sinθ = 0.
So, there will be no magnetic force on stationary charge.
Magnetic force depends on angle between v and 𝐁
v
B
𝐂𝐚𝐬𝐞 −2 :
𝛉 = 𝟗𝟎°
𝐅𝐦𝐚𝐱 = 𝐪𝐯𝐁
𝐂𝐚𝐬𝐞 −𝟏 :
𝛉 = 𝟎° 𝐨𝐫 𝟏𝟖𝟎°
𝐅 = 𝟎
v
B
v
B
(θ can vary from 0° to 180°)

11. Right hand thumb rule :
Right hand thumb rule :
Direction of force
Direction of force
Point the fingers of right hand in the direction of v,
and curl them towards 𝐁 then thumb will give the direction of v × 𝐁
For force on negative charge, just reverse the final direction.
Note

12. Work done by magnetic
field on any charge is
always ZERO!!
Work done by magnetic
field on any charge is
always ZERO!!
Ԧ
𝐅 ∙ 𝐯 = 0
𝚫𝐊𝐄 = 0
v
B
θ
Ԧ
𝐅 ⊥ 𝐯 Ԧ
𝐅 ⊥ 𝐁
Power :
Power :
Ԧ
𝐅 ∙ 𝐝Ԧ
𝐬 = 0
Work :
Work :
Important
Ԧ
𝐅 = 𝐪(𝐯 × 𝐁)
We know that

13. Find the direction of force in each case.
Example
Example
v
I
x
(a)
v
I
x
(b)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

14. In presence of external Magnetic field (only)-
1. Can speed of a moving charge change?
2. Can direction of a moving charge change?
3. Can velocity of a moving charge change?
4. Can a stationary charge start moving?
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

15. A particle has charge +2C and it moves with velocity 𝟐 Ƹ
𝐢 + 𝟑 Ƹ
𝐣 + መ
𝐤 𝐦/𝐬. It
enters a magnetic field Ƹ
𝐢 − 𝟒 Ƹ
𝐣 − መ
𝐤 𝐓. Find the force due to magnetic field
applied on it.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

16. B
Find the direction in which charged particle will experience force.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

17. B
Find the direction in which charged particle will experience force.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

18. B
1
2
3
From the path followed, identify nature of charge on the particle.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

19. Example
Example
A current of 2A is flowing through a coil of radius 10 cm. A proton is
moving in the plane of coil with speed of 𝟓 × 𝟏𝟎𝟒 m/s then find force on
the charge particle when it passes through its centre.
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

20. Find the acceleration of charged particle
when it is at r distance from wire.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
(q, m)
v
I

21. Find force on particle (q, m) due to magnetic field.
Example
Example
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧
𝐯
I
𝟑𝐑
1. 𝐯
I
𝟑𝐑
2.
𝐑 𝐑