**Exercise 20.6**

Part A = 0.33 m^{2}

Part B = 42 V

Part C = 83 V

**Solutions Below:**

Part A

Express your answer using two significant figures.

The induced emf is just the change in magnetic flux per unit time. Start by finding the magnetic flux through the loop:

ΔΦ = A * ΔB

Where A is the area of the loop (0.40 m * 0.40 m = 0.16 m^{2})

So:

ΔΦ = A * 0.25

The formula for emf (ε) is:

ε = ΔΦ / Δt

Substitute in for ΔΦ and the voltage and time that the problem gave us:

83 = (A * 0.25) / 0.001

83 = 250 * A

A = 0.332 m^{2}

Round to 2 significant figures:

0.33 m^{2}

Part B

Express your answer using two significant figures.

Just use the same formula as in Part A:

ε = ΔΦ / Δt

ε = (A * 0.25) / 0.002

ε = (0.332 * 0.25) / 0.002

ε = 41.5

Note that mastering physics is picky (as usual) about this problem. If you used the 0.33 m^{2} for area that you found in Part A, you’ll get the wrong answer. You have to plug in the unrounded 0.332 m^{2}, get 41.5 V, and then round up to 42 V.

42 V

Part C

Express your answer using two significant figures.

Just use the same formula as in Part A:

ε = ΔΦ / Δt

ε = (0.332 * 0.50) / 0.002

ε = 83

83 V