A conducting square loop is placed in a magnetic field `B` with its plane perpendicular to the field. Now 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

Options

A. `2aalphaB`
B. `a^2alphaB`
C. `2a^2alphaB`
D. `aalphaB`

Answer

A

Explanation

At time `t`
Side of square `i=l_i-dt`
`S=l^2=(l_i-alphat)^2`
At given time
`l=l_i-alphat=a`
`phi=BS=B(l_i-alphat)^2`
`e=|(dphi)/(dt)|=2Balpha(l_i-alphat)`
But,`(l_i-alphat)=a`
`:. e=2a alpha B`