MHT CET · Physics · Electromagnetic Induction
A conductor \(10 \mathrm{~cm}\) long is moved with a speed \(1 \mathrm{~m} / \mathrm{s}\) perpendicular to a field of strength 1000 \(\mathrm{A} / \mathrm{m}\). The e.m.f. induced in the conductor is [Given : \(\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\) ]
- A \(\pi \mathrm{mV}\)
- B \(2 \pi \mathrm{mV}\)
- C \(40 \pi \mu \mathrm{V}\)
- D \(4 \pi \mu \mathrm{V}\)
Answer & Solution
Correct Answer
(C) \(40 \pi \mu \mathrm{V}\)
Step-by-step Solution
Detailed explanation
Motional emf
\(\mathrm{e}=\mathrm{Bv} \mathrm{l}\)
Magnetic field \(B=\mu_0 H\)
\(\therefore \quad \mathrm{e}=\mu_0 \mathrm{H} \mathrm{v} l\)
\(\begin{aligned} & \mathrm{e}=4 \pi \times 10^{-7} \times 1000 \times 0.01 \times 1 \\ & \mathrm{e}=40 \pi \mu \mathrm{V}\end{aligned}\)
\(\mathrm{e}=\mathrm{Bv} \mathrm{l}\)
Magnetic field \(B=\mu_0 H\)
\(\therefore \quad \mathrm{e}=\mu_0 \mathrm{H} \mathrm{v} l\)
\(\begin{aligned} & \mathrm{e}=4 \pi \times 10^{-7} \times 1000 \times 0.01 \times 1 \\ & \mathrm{e}=40 \pi \mu \mathrm{V}\end{aligned}\)
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