Let's suppose we have a rectangular loop of wire (one single loop) with a width of W = 2.00 cm and a length of L = 6.20 cm. The loop has a resistance of 148.00 Ohms. Initially we also have a magnetic field pointing straight through the loop with magnitude B = 0.70 T. Now we turn up the magnetic field over a time interval of t = 2.20 s. The final magnitude of the magnetic field is 2.90 T. What is the magnitude of the average induced EMF over that time interval?

0.00124 V

Explanation:

Parameters given:

Width of loop, W = 2 cm = 0.02 m

Length of loop, L = 6.2 cm = 0.062 m

Initial magnetic field, Bini = 0.7 T

Final magnetic field, Bfin = 2.9 T

Time interval, dt = 2.2 secs

The magnitude of the average induced EMF due to a changing magnetic field in a time interval, dt, is given as:

EMF = | -(N * A * dB) / dt |

Where N = number of loops = 1

A = area of loop = L * W = 0.02 * 0.062 = 0.00124 m²

dB = change in magnetic field = Bfin - Bini = 2.9 - 0.7 = 2.2 T

=> EMF = | -(1 * 0.00124 * 2.2) / 2.2 |

EMF = | -0.00124 |

EMF = 0.00124 V

The average induced EMF is 0.00124 V

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