AP EAMCET · PHYSICS · Magnetic Effects of Current

Two concentric coils each of radius equal to $4 π cm$ are placed at right angles to each other. If $10 A$ and $24 A$ are the currents flowing through the coils, respectively, the magnetic induction at the center of the coils will be

A $13 \times 10^{- 5} Wb m^{- 2}$
B $12 \times 10^{- 5} Wb m^{- 2}$
C $7 \times 10^{- 5} Wb m^{- 2}$
D $5 \times 10^{- 5} Wb m^{- 2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $13 \times 10^{- 5} Wb m^{- 2}$

Step-by-step Solution

Detailed explanation

Magnetic field due to the coil, B1=μ0i2r ⇒B1=μ0×1024π×10-2=μ0×10×1028π ⇒B1=10×10-52=5×10-5 T similarly, ⇒B2=24×10-52=12×10-5 T ⇒B=B12+B22=13×10-5 wb m-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.

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Two concentric coils each of radius equal to 4πcm are placed at right angles to each other. If 10 A and 24 A are the currents flowing through the coils, respectively, the magnetic induction at the center of the coils will be

Step-by-step Solution

Two concentric coils each of radius equal to $4 π cm$ are placed at right angles to each other. If $10 A$ and $24 A$ are the currents flowing through the coils, respectively, the magnetic induction at the center of the coils will be