Question

The length of a solenoid is 0.1 m and its diameter is very small. A wire is wound over it in two layers. The numbers 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:

• A. $3.4\times {10}^{-3}tesla$
• B. $3.4\times {10}^{-3}gauss$
• C. $3.4\times {10}^{3}tesla$
• D. $3.4\times {10}^{3}gauss$

Answer 1

The correct option is A $3.4\times {10}^{-3}tesla$

Since diameter is very small in comparison to length of solenoid.
So it behaves like infinite solenoid.
So $B_{net}={\mu }_0\frac{i}{l}(n_1+n_2)$

$=4\pi \times {10}^{-7}\times \frac{3}{0.1}(40+50)$
$=3.4\times {10}^{-3}T$