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Physics Question on Moving charges and magnetism

A circular coil of radius 40 mm consists of 250 turns of wire in which the current is 20mA. The magnetic field in the center of the coil is μ=4π?10−7Hm−1\mu =4\pi?10^{-7}Hm^{-1}

A

0.785 G

B

0.525 G

C

0.629 G

D

0.900 G

Answer

0.785 G

Explanation

Solution

In a circular coil of n turns, magnetic field is
B=μ0nI2r=4π?10−7?250?20?10−32?40?10−3B=\frac{\mu_0nI}{2r}=\frac{4\pi?10^{-7}?250?20?10^{-3}}{2? 40?10^{-3}}
(∵(\because n = no. of turns, I = current through
coil, r = radius of coil)
⇒B=4π?250?20?10−7−3+32?40\Rightarrow B=\frac{4\pi ?250 ?20?10^{-7-3+3}}{2?40}
=250?3.14?10−710^{-7}
=785?10−7=0.785?10−4=785?10^{-7}=0.785?10^{-4}tesla
=0.785 gauss