Magnetic Effects & Magnetism

JEE Main level, single correct, medium

83 of 276

Question 83 of 276

One of the two identical conducting wires of length LL is bent in the form of a circular loop and the other one into a circular coil of NN identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop (BL)\left({B}_{L}\right) to that at the centre of the coil (BC),\left({B}_{C}\right), i.e. BLBC\dfrac{{B}_{L}}{{B}_{C}} will be

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Answer: (A) 1N2\dfrac{1}{{N}^{2}}

For a single loop, radius

r1=L2π{r}_{1}=\dfrac{L}{2\pi }

BL=μ0I2r1=μ0I2L×2π{B}_{L}=\dfrac{{\mu }_{0}I}{2{r}_{1}}=\dfrac{{\mu }_{0}I}{2L}\times 2\pi ...(1)

For a circular coil, radius

r2=L2πN{r}_{2}=\dfrac{L}{2\pi N}

Bc=μ0IN2r2=μ0IN2L2πN{B}_{c}=\dfrac{{\mu }_{0}IN}{2{r}_{2}}=\dfrac{{\mu }_{0}IN}{2L}2\pi N ...(2)

BLBC=1N2\dfrac{{B}_{L}}{{B}_{C}}=\dfrac{1}{{N}^{2}} (from eqns (1) and (2))

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