Question

For each of the following problems, write up your solutions using the 4-step problem solving procedure (get started, plan, execute, evaluate) that is detailed in the problem set rubric. Please include sketches of the problem and words describing the steps, not just the math.

3. Design a current loop that, when rotated in a uniform magnetic field of strength 0.1 T, will produce an emf of ε=ε0 sinωt, where ε0 =110V and ω=120π rad/s.

Answer 1

We have to design a current loop such that when it is rotated in uniform magnetic field will produce emf as given in question.

When Magnetic Flux passing through a loop changes with time, this caused the generation of induces emf in the loop. The induced emf is given by,

Here Magnetic Flux,

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If we rotate the loop with a angular frequency the angle will keep on change, hence the Flux will also change with time

Now

This is the same expressions of induced emf as given in question if we set

Here,

Now we may find area of loop as,

We can have any geometry possible for this loop but we need to rotate it with the given angular frequency to obtain given emf, if we keep loop circular then the radius corresponding to such area will be,