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Physics Question on Moving charges and magnetism

A closely wound solenoid 80 cm80 \,cm long has 55 layers of winding of 400400 turns each. The diameter of the solenoid is 1.8 cm1.8\, cm. If the current carried is 8.0 A8.0\, A, the magnitude of BB inside the solenoid near its centre will be

A

8π×10−3 T8\pi \times 10^{-3}\,T

B

6π×10−3 T6\pi \times 10^{-3}\,T

C

4π×10−3 T4\pi \times 10^{-3}\,T

D

3π×10−3 T3\pi \times 10^{-3}\,T

Answer

8π×10−3 T8\pi \times 10^{-3}\,T

Explanation

Solution

The magnitude of B⃗\vec{B} inside the solenoid near its centre is
B=μ0nIB=\mu_{0} n I
Here, μ0=4π×10−7 T mA−1\mu_{0}=4 \pi \times 10^{-7}\, T\, m A^{-1}
n=n= Number of turns per unit length of the solenoid
= Total number of turns  Length of the solenoid =\frac{\text { Total number of turns }}{\text { Length of the solenoid }}
=5×40080×10−2m−1=\frac{5 \times 400}{80 \times 10^{-2}} m^{-1}
I=8.0 AI=8.0 \,A (Given)
∴B=4π×10−7×5×40080×10−2×8\therefore B=4 \pi \times 10^{-7} \times \frac{5 \times 400}{80 \times 10^{-2}} \times 8
=8π×10−3 T=8 \pi \times 10^{-3}\, T