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Q.

A conducting L –shaped rod $A B C$ is rotated with uniform angular speed $ω$ in uniform magnetic field $B_{0}$ with the help of two identical strings about an axis shown in the figure. Potentials at $A, B, C$ and $D$ are $V_{A}, V_{B}, V_{C}$ and $V_{D}$ respectively. $O A = O C = A B = B C = l,$ $D is mid point of A B, \vec{ω}$ is directed opposite to $\vec{B}$ . Then

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a

$V_{B} - V_{C} = \frac{1}{2} B_{0} ω l^{2}$

b

$V_{A} - V_{C} = z e r o$

c

$V_{A} - V_{D} = \frac{1}{8} B_{0} ω l^{2}$

d

$V_{A} - V_{B} = \frac{1}{2} B_{0} ω l^{2}$

answer is A, C, D.

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Detailed Solution

$d ε_{\ln} = (\bar{V} \times \bar{B}) . \bar{d L} = x ω B d x ε_{\ln} = \int_{r_{1}}^{r_{2}} x d x ω B$

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A conducting L –shaped rod ABC is rotated with uniform angular speed ω in uniform magnetic field B0with the help of two identical strings about an axis shown in the figure. Potentials at A,B,C and D are VA,VB,VC and VD respectively. OA=OC=AB=BC=l, D is mid point of AB,ω→ is directed opposite to B→. Then