Question

The magnetic field in a region is given by $\vec{ B }= B _{0}\left(\frac{ x }{ a }\right) \hat{ k }$. A square loop of side $d$ 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:

• A. $\frac{ B _{0} v _{0}^{2} d }{2 a }$
• B. $\frac{ B _{0} v _{0} d }{2 a }$
• C. $\frac{ B _{0} v _{0} d ^{2}}{ a }$
• D. $\frac{ B _{0} v _{0} d ^{2}}{2 a }$

Answer 1

Answer: (C)

$E _{1}=\frac{ B _{0}( x + d )}{ a } v _{0} d$
$E _{2}=\frac{ B _{0}( x )}{ a } v _{0} d$
$E _{ net }= E _{1}- E _{2}$
$E _{ net }=\frac{ B _{0} v _{0} d ^{2}}{ a }$