TS EAMCET · Physics · Magnetic Effects of Current

Two circular loops $L_{1}$ and $L_{2}$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_{1}$ is $R_{1}$ and that of $L_{2}$ is $R_{2}$ . The distance between the centres of the loops is $\sqrt{3} R_{1}$ . The magnetic field at the centre of $L_{2}$ shall be zero if

A $R_{2} = 4 R_{1}$
B $R_{2} = 2 R_{1}$
C $R_{2} = \sqrt{2} R_{1}$
D $R_{2} = 8 R_{1}$

Verified Solution

Answer & Solution

Correct Answer

(D) $R_{2} = 8 R_{1}$

Step-by-step Solution

Detailed explanation

Net magnetic field at centre, Bnet=B1-B2 For magnetic field, Bnet to be zero, B1=B2 Magnetic field at the axis of coil 1 at a distance of 3R1 B1=μ0i2πR124πR12+3R123/2 B1=μ0i16R1 ...1 Magnetic field at the centre of coil 2.…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

Two circular loops L1 and L2 of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop L1 is R1 and that of L2 is R2. The distance between the centres of the loops is 3R1. The magnetic field at the centre of L2 shall be zero if

Step-by-step Solution