One of the two identical conducting... | Moving Charges & Magnetism

JEE MAIN 2019

09-01-19 S2

Question

One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $\left(B_L\right)$ to that at the centre of the coil $\left(B_C\right)$, i.e. $\frac{B_L}{B_C}$ will be

Select the correct option:

$\frac{1}{N}$

$\mathrm{N}^2$

$\frac{1}{\mathrm{~N}^2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{array}{lll}r_1=\frac{L}{2 \pi} & \Rightarrow & \left.B_L=\frac{\mu_0 I}{2 \pi} \right\rvert\, \\ r_2=\frac{L}{2 N \pi} & \Rightarrow & B_C=\frac{N \mu_0 I}{2 r_2} \\ \frac{B_L}{B_C}=\frac{1}{N^2} & & \end{array}$

Question Tags

JEE Main

Physics

Medium

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