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Question

# As shown in the figure, the rod is moving with velocity, 2 m/s. What will the value of velocity v after time t ? (Given: B=3 T, and length of rod =1 m, mass of rod =m).

A
2e3t/m
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B
2e3t/m
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C
2e6t/m
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D
26mt
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Solution

## The correct option is D 2−6mtThe emf induced in a straight conductor of length l moving with velocity v in a magnetic field of intensity B is given by, E=Blv The resistors are forming a Wheatstone Bridge. ∴ The equivalent resistance between P and Q is, RPQ=62=3 Ω Current in the circuit, i=ERPQ (clockwise) ⇒i=BlvRPQ ∴ Force experienced by the moving conductor due to magnetic field, →FB=i(→l×→B)=ilB ⇒FB=(Blv)×(lB)RPQ=B2l2vRPQ Substituting the values, FB=32×12×23=6 N (Opposite to velocity ) Now, acceleration, a=−FBm ⇒∫v2dv=−6m∫t0dt ⇒v−2=−6mt ∴v=2−6mt Hence, option (D) is correct.

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