First slide

Motional EMF

Question

A square loop of side a is placed such that its plane is the same as that of a very long straight wire carrying a current I. The centre O of the loop is at a distance x from the wire. The loop is given a velocity v as shown. If x >> a, the magnitude of the emf induced in the loop is proportional to

Difficult

A

$x$
B

$x^{2}$
C

$\frac{1}{x}$
D

$\frac{1}{x^{2}}$

Solution

$B = \frac{μ_{0} i}{2 π x} ϕ = B A = B a^{2} e = - \frac{d ϕ}{d t} = - \frac{d}{d t} (\frac{μ_{0} i}{2 π x}) a^{2} = - \frac{μ_{0} i}{2 π} (- \frac{1}{x^{2}}) \frac{d x}{d t} a^{2} e = \frac{μ_{0} i}{2 π} (\frac{1}{x^{2}}) v a^{2}$

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