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Question: A plane circular loop of conducting wire of radius cm which possesses turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of with respect to the normal direction to the loop. The magnetic field-strength is increased at a constant rate from T to T in a time interval of s. What is the emf generated around the loop? If the electrical resistance of the loop is , what current flows around the loop as the magnetic field is increased?

Answer: The area of the loop is

The component of the magnetic field perpendicular to the loop is

where is the magnetic field-strength. Thus, the initial magnetic flux linking the loop is

Likewise, the final flux linking the loop is

The time rate of change of the flux is

Thus, the emf generated around the loop is

Note, incidentally, that one weber per second is equivalent to one volt.

According to Ohm's law, the current which flows around the loop in response to the emf is

Next: Worked Example 2: Lenz's Up: Magnetic Induction Previous: Worked Examples
Richard Fitzpatrick 2007-07-14