The magnetic field in a region is given by ve | vedclass

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(A) The magnetic field is $\vec B = B_0(1 + \frac{x}{a})\hat k$. The loop moves with velocity $\vec V = V_0\hat i$ in the $xy$-plane.For side $(1)$ at

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$\frac{V_0 B_0 d^2}{a}$

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(A) The magnetic field is $\vec B = B_0(1 + \frac{x}{a})\hat k$. The loop moves with velocity $\vec V = V_0\hat i$ in the $xy$-plane.For side $(1)$ at $x = 0$,the magnetic field is $B_1 = B_0(1 + 0) = B_0$. The induced $emf$ is $e_1 = B_1 V_0 d = B_0 V_0 d$.For side $(2)$ at $x = d$,the magnetic field is $B_2 = B_0(1 + \frac{d}{a})$. The induced $emf$ is $e_2 = B_2 V_0 d = B_0(1 + \frac{d}{a}) V_0 d = B_0 V_0 d + \frac{B_0 V_0 d^2}{a}$.Sides $(3)$ and $(4)$ are parallel to the velocity vector,so the induced $emf$ in these sides is zero.The net $emf$ induced in the loop is $e = |e_2 - e_1| = |(B_0 V_0 d + \frac{B_0 V_0 d^2}{a}) - B_0 V_0 d| = \frac{B_0 V_0 d^2}{a}$.

The magnetic field in a region is given by $\vec B = B_0(1 + \frac{x}{a})\hat k$. $A$ square loop of edge length $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec V = V_0\hat i$. The $emf$ induced in the loop is:

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