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Q.

The length of the solenoid is 0.1m and its diameter is very small. A wire is wound over in two layers. The number of turns in the inner layer is 50 and that on the outer layer is 40. The strength of current flowing in two layers in the same direction is 3 ampere. The magnetic induction in the middle of the solenoid will be

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a

$3.4 \times 10^{- 3} gauss$

b

$3.4 \times 10^{3} gauss$

c

$3.4 \times 10^{3} T$

d

$3.4 \times 10^{- 3} T$

answer is A.

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Detailed Solution

$B = μ_{0} ni \Rightarrow B_{net} = \frac{μ_{0} i (N_{1} + N_{2})}{l} = \frac{4 π \times 10^{- 7} \times 3 (40 + 50)}{0 .1}$

$\Rightarrow B_{net} = 3 .4 \times 10^{- 3} T$

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The length of the solenoid is 0.1m and its diameter is very small. A wire is wound over in two layers. The number of turns in the inner layer is 50 and that on the outer layer is 40. The strength of current flowing in two layers in the same direction is 3 ampere. The magnetic induction in the middle of the solenoid will be