The magnetic field in a region is given by \(\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }\). 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 \(\overrightarrow{ v }= v _{0} \hat{ i }\). The emf induced in the loop is:

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{ B _{0} v _{0} d ^{2}}{ a }\)

Detailed explanation

\(E _{1}=\frac{ B _{0}( x + d )}{ a } v _{0} d\)

\(E _{2}=\frac{ B _{0}( x )}{ a } v _{0} d\)

\(E _{ net }= E _{1}- E _{2}\)

\(E _{ net }=\frac{ B _{0} v _{0} d ^{2}}{ a }\)

Same subject

List \(I\)	List \(II\)
\(A\) Troposphere	\(I\) Approximate \(\quad 65-75\, km\) over Earth's surface
\(B\) E-Part of Stratosphere	\(II\) Approximate \(300\,km\) over Earth's surface
\(C\) \(F _2\)-Part of Thermosphere	\(III\) Approximate \(10\,km\) over Earth's surface
\(D\) \(F _2\)-Part of Thermosphere	\(IV\) Approximate \(100\,km\) over Earth's surface

From JEE Mains