Question

A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate \(\alpha \) The induced emf in the loop at an instant when its side is 'a' is
A) \(2a\alpha B\)
B) \({{a}^{2}}\alpha B\)
C)\(2{{a}^{2}}\alpha B\)
D)\(a\alpha B\)

Answer 1

Correct solution is option A ) \(2a\alpha B\) 

Explaination: 

"a" at any time "t" , the side of the square a= \((a_0-\alpha_t)\) , where \(\alpha_0\) side at t=0 . 

at this instant , flux through the square 

⇒\(\phi = BA\cos0^o = B(a_o-\alpha_t)^2 \)

⇒\(\therefore emf \ induced \ E= -\frac{d\phi}{dt}\) 

⇒\(E=-B\times 2 (a_0-\alpha_t)\) 

⇒E= \(2a\alpha B\)