Question

A uniform field `B` increasing with time exists in a cylindrical region of centre `O` and radius `R`. The direction of magnetic field is inwards the paper as shown. The work done by external agent in taking a unit positive charge slowly from `A` to `C` via paths `APC, AOC` and `AQC` be `W_(APC), Q_(AOC)` and `W_(AQC)` respectively. Then-

A. `W_(APC) = W_(AOC) = W_(AQC)`
B. `W_(APC) gt W_(AOC) gt W_(AQC)`
C. `W_(APC) lt W_(AOC) lt W_(AQC)`
D. `W_(APC) = W_(AQC) lt W_(AOC)`

Answer 1

Correct Answer - B
Because of increase in magnetic field with time, electric field is induced in the circular region and represented by lines of forces as shown in figure. The signs of minimum work done by external agent in taking unit positive charge from `A` to `C` via path `APC, AOC` and `AQC` are

`W_(APC) = -ve, W_(AOC) = 0, W_(AQC) = +ve`
( C) is the correct choice.