To practice Problem-Solving Strategy 25.1 Electromagnetic induction. A loop of w

Question

To practice Problem-Solving Strategy 25.1 Electromagnetic induction.

A loop of wire of radius a = 35 mm has an electrical resistance R = 0.035 . The loop is initially inside a uniform magnetic field of magnitude B0 = 1.9 T parallel to the loop's axis. The magnetic field is then reduced slowly at a constant rate, which induces a current I = 0.35 A in the loop. How long does it take for the magnitude of the uniform magnetic field to drop from 1.9 T to zero?

PROBLEM-SOLVING STRATEGY 25.1 Electromagnetic induction

Faraday’s law allows us to find the magnitude of induced emfs and currents; Lenz’s law allows us to determine the direction.

PREPARE Make simplifying assumptions about wires and magnetic fields. Draw a picture or a circuit diagram. Use Lenz's law to determine the direction of the induced current.

SOLVE The mathematical representation is based on Faraday's law

E=t.

For an N-turn coil, multiply by N. The size of the induced current is I=E/R.

ASSESS Check that your result has the correct units, is reasonable, and answers the question.

Prepare

Assume that at any time the magnetic field is uniform inside the coil and that, when the field is decreased, it changes magnitude but not direction. Note that the resistance of the coil and the induced current are assumed to be constant and of known magnitudes.

Electromagnetic induction. A loop of wire of radius a S 35 mm has an electrical resistance R 30.035 n. The loop is initially inside a uniform magnetic field of magnitude Bo 9 TP parallel to the loop's axis. The magnetic field is then reduced slowly at a constant rate, which induces a current I 0.35 A in the loop. How long does it take for the magnitude of the uniform magnetic field to drop from 1.9 T to zero? Figure 1 of 1 x x x x Use the mathematical representation of Faraday's law to help solve this problem. Part C Find the time At it takes the magnetic field to drop to zero. Express your answer in seconds using three significant figures. At 34 Submit Hints My Answers Give Up Review Part incorrect Try Again Assess Check to see that your final result makes sense. Part D

Explanation / Answer

a = 35mm , Bo =1.9 T, B =0 , I =0.35 A, R =0.035 ohms

From ohms law V = IR

V = 0.35*0.035

from faradays law induced emf V = -d(phi)/dt

V = A(Bo -B)/Dt

0.35*0.025 = 3.14*0.035^2*1.9/dt

Dt = 0.835 s

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