JEE MAIN - Physics (2022 - 26th July Morning Shift - No. 7)
$$\mathrm{B}_{X}$$ and $$\mathrm{B}_{\mathrm{Y}}$$ are the magnetic fields at the centre of two coils $$\mathrm{X}$$ and $$\mathrm{Y}$$ respectively each carrying equal current. If coil $$X$$ has 200 turns and $$20 \mathrm{~cm}$$ radius and coil $$Y$$ has 400 turns and $$20 \mathrm{~cm}$$ radius, the ratio of $$B_{X}$$ and $$B_{Y}$$ is :
1 : 1
1 : 2
2 : 1
4 : 1
Explanation
$$B = {{{\mu _0}NI} \over {2R}}$$
$${{{B_X}} \over {{B_Y}}} = {{{N_x}{R_y}} \over {{N_y}{R_x}}}$$
$$ = {{200 \times 20} \over {400 \times 20}} = {1 \over 2}$$
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