Charges & Magnetism Test

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Charges & Magnetism Test - 18

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Question 1
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A solenoid of length 0.6 m has a radius of 2 cm and is made up of 600 turns. If it carries a current of 4A, then the magnitude of the magnetic field inside the solenoid is

A
6.024 x 10^-3 T

B
8.024 x 10^-3 T

C
5.024 x 10^-3 T

D
7.024 x 10^-3 T

Solution

Here, n = 600/0.6 = 1000 turns/m, I = 4A
l = 0.6m, r = 0.02 m ∵ 1/r = 30 i.e., l >>r
Hence, we can use long solenoid formuls, then
∴ B = μ₀nI = 4π x 10^-7 x 10³ x 4 = 50.24 x 10^-4
= 5.024 x 10^-3T
Question 2
1 / -0

A solenoid of length 50 cm, having 100 turns carries a current of 2.5 A. The magnetic field at one end of the solenoid is

A
3.14 x 10^-4 T

B
6.28 x 10^-4 T

C
1.57 x 10^-4 T

D
9.42 x 10^-4 T

Solution

Here, I = 2.5 A , I = 50 cm = 0.50 m and n = 100/0.50 = 200 m^-1
∴
Question 3
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A 90 cm long solenoid has six layers of windings of 450 turns each. If the diameter of solenoid is 2.2 cm and current carried is 6A, then the magnitude of magnetic field inside the solenoid, near its centre is

A
50π G

B
60π G

C
72π G

D
80π G

Solution

For six layers of windings the total number of turns = 6 x 450 = 2700
Now number of turns per unit length

Then the field in side the solenoid near the centre
B = μ₀nI = 4π x 10^-7 x 3000 x 6 = 72π x 10^-4 T = 72πG
Question 4
1 / -0

Which of the following statement is correct?

A
The magnetic field in the open space inside the toroid is constant.

B
The magnetic field in the open space exterior to the toroid is constant.

C
The magnetic field inside the core of toroid is constant.

D
The magnetic field inside the core of toroidis zero.

Solution

Option C is incorrect as magnetic field inside the core of the toroid varies greatly.
Question 5
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The inner and outer radius of a toroid core are 28 cm and 29 cm respectively and around the core 3700 turns of a wire are wounded. If the current in the wire is 10A, then the magnetic field inside the core of the toroid is

A
2.60 x 10^-2T

B
2.60 x 10^-3T

C
4.52 x 10^-2T

D
4.52 x 10^-3T

Solution

The number of turns per unit length for the given toroid n = N/2πr_av
The average radius of toroid
r_av = (28 + 29)/2 = 28.5 cm 28.5 x 10^-2m