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A straight rod of length $0.5\,\text{m}$ moves with a velocity of $4\,\text{m/s}$ perpendicular to a uniform magnetic field of $0.2\,\text{T}$, with its length perpendicular to both $\vec{v}$ and $\vec{B}$. The motional EMF developed across its ends is:
A$0.4\,\text{V}$
B$0.2\,\text{V}$
C$0.1\,\text{V}$
D$1.0\,\text{V}$
Answer & Solution
Correct answer: A. $0.4\,\text{V}$
Motional EMF $\varepsilon = B v \ell = 0.2 \times 4 \times 0.5 = 0.4\,\text{V}$. This follows from the magnetic Lorentz force on the free charges in the moving rod separating them until an electrostatic force balances the magnetic one.
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