Magnetic Effects & Magnetism

JEE Main level, single correct, medium

20 of 276

Question 20 of 276


Two identical circular loops PP and QQ each of radius rr are lying in parallel planes such that they have common axis. The current through PP and QQ are II and 4I4 I respectively in clockwise direction as seen from OO. The net magnetic field at OO is:

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Answer: (A) 3μoI42r\frac{3 \mu_{\mathrm{o}} I}{4 \sqrt{2} r} towards QQ

Two identical circular loops P and Q, each of radius rr, are separated by distance rr along their common axis. Current in P is II and in Q is 4I4I (both clockwise as seen from O).
Point O is at the midpoint. The magnetic fields from each loop at O:
B1=μ0IR22(R2+R2)3/2B_1 = \frac{\mu_0 I R^2}{2(R^2 + R^2)^{3/2}} (from P, pointing toward Q)
B2=4μ0IR22(R2+R2)3/2B_2 = \frac{4\mu_0 I R^2}{2(R^2 + R^2)^{3/2}} (from Q, pointing toward P)
Bnet=B2−B1=3μ0IR22(2R2)3/2=3μ0I42RB_{net} = B_2 - B_1 = \frac{3\mu_0 I R^2}{2(2R^2)^{3/2}} = \frac{3\mu_0 I}{4\sqrt{2}R}
Direction: towards Q.

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