# To find work done by time-varying magnetic field

1. Apr 20, 2010

### hermy

1. The problem statement, all variables and given/known data

Magnetic field in the cylindrical region with its axis passing through O varies at a constant rate x. A triangular imaginary loop ABC, with AB = BC, is lying in this region as shown in figure. The work done to move unit positive charge from A to B along side AB is:

(a) r2 x

(b) $$\pi$$ r2 x

(c) r2/2 x

(d) 3r2/4 x

2. Relevant equations

emf induced in a circular loop of radius a due to time varying magnetic field = $$\pi$$ a2 x

work done in moving a charge q = qV

3. The attempt at a solution

Honestly, I have no clue how to go about it. Electric field is non-conservative, so we cant simply find the potential difference. When I tried to integrate E.dl , I could not find the angle between electric field and displacement. I feel pretty sure that we need to integrate, but how? A hint would be sufficient.

#### Attached Files:

• ###### q 39.bmp
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2. Apr 21, 2010

### Eloy

You can use Faraday's law: integral of E dl (induced electromotive force) is equal to the time rate of change of the magnetic flux through the loop. You will only need to calculate area of the triangle, so no integration is necessary.

3. Apr 21, 2010

### hermy

i got it. so the answer should be (c). thanks eloy.