Figure. shows three rigions of magnetic field each of area `A`, and in each rigion, magnitude of mqagnetic field decreases rate `alpha`. If `vec(E)` is the induced electric field, then the vlue of the line `ointvec(E).dvec(r )` along the given loop is equal to

Options

A. (a) `alphaA`
B. (b) `-alphaA`
C. ( c) `3alphaA`
D. (d) `-3alphaA`

Answer

B

Explanation

(b) As anticlockwise direction is positive, so area vector out wards is positive. So net flux through the given loop is
`phi = -BA - BA + BA = -BA`
`ointvec(E).vec(dr) = -(dphi)/(dt) = -(d(-BA))/(dt) = A(dB)/(dt) = A(-alpha)`
`rarr` `ointvec(E).vec(dr) = - alphaA`