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Question

A toroidal solenoid has 3000 turns and a mean radius of 10 cm. It has a soft iron core of relative permeability 2000. What is the magnitude of the magnetic field in the core when a current of 1 A is passed through the solenoid ?


A
0.012T
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B
0.12T
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C
1.2T
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D
12T
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Solution

The correct option is D $$12 \mathrm { T }$$
$$Given:$$ $$N = 3 0 0 0$$
$$r = 1 0 c m = 0 . 1 m$$
$$n =\frac{ N }{ 2 \pi r }$$
$$\mu _{ r }= 2 0 0 0$$
$$I = 1 A$$ 
$$Solution:$$ 
For a solenoid magnetic field, $$B =\mu n I =$$$$\mu_{r} \mu_{0} n I$$
$$B=2000 \times 4 \pi \times 10^{-7} \times \frac{N}{2 \pi r} \times 1$$

$$=2000 \times 4 \times 10^{-7} \times \frac{3000}{2 \pi \times 0.1} \times 1=12 T$$
$$So,the$$ $$correct$$ $$option:D$$


Physics

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