KCET · Physics · Electromagnetic Induction

A metallic rod of length \(1 \mathrm{~m}\) held along east-west direction is allowed to fall down freely. Given horizontal component of earth's magnetic field \(B_H=3 \times 10^{-5} \mathrm{~T}\). the emf induced in the rod at an instant \(t=2 \mathrm{~s}\) after it is released is
(Take, \(g=10 \mathrm{~ms}^{-2}\) )

A \(6 \times 10^{-4} \mathrm{~V}\)
B \(3 \times 10^{-3} \mathrm{~V}\)
C \(3 \times 10^{-4} \mathrm{~V}\)
D \(6 \times 10^{-3} \mathrm{~V}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(3 \times 10^{-4} \mathrm{~V}\)

Step-by-step Solution

Detailed explanation

Given, \(B_H=3 \times 10^{-5} \mathrm{~T}\)
\(l=1 \mathrm{~m}\)
Height travelled by rod in \(t=2 \mathrm{~s}\)
\(h=\frac{1}{2} g t^2=\frac{1}{2} \times 10 \times 2^2=20 \mathrm{~m}\)
\(\therefore\) Speed of rod, \(v=\frac{h}{t}=\frac{20}{2}=10 \mathrm{~m} / \mathrm{s}\)
Hence, induced emf
\(\begin{aligned} e & =B_H v l=3 \times 10^{-5} \times 10 \times 1 \\ & =3 \times 10^{-4} \mathrm{~V}\end{aligned}\)

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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