CK-12-Physics - Intermediate

http://www.ck12.org Chapter 19. Electromagnetism

Check Your Understanding

1. A coil of wire with 20 loops and cross-sectional area 25cm^2 is stationary in a constant magnetic field of 0.90T.
   The angle between the magnetic fieldBand the area vectorAis 45◦. What is the induced voltage in the coil?
   Answer: This is a bit of a tricky question because specific values were cited, but none were required to find the
   answer. There is no relative motion between the coil and the magnetic field. Since the coil is stationary, the flux
   through the coil is constant. The rate of change of the flux is therefore zero, as is the induced voltage.


2. If the south pole of a magnetic is pushed toward the center of a coil, what is the direction of the induced current
   in the coil?
   Answer: According to Lenz’s law, the induced current must produce a magnetic field that would prevent the flux
   from increasing. The magnetic field must be equivalent to the field of a magnet with its “south pole” facing the
   incoming south pole of the magnet. To determine the direction of the induced current, we position the right hand so
   that the thumb would point away from the incoming magnet. The direction of the current would be the same as the
   direction in which the fingers are curled.

Illustrative Example 1

a. Magnetic field lines pass perpendicularly through a circular loop of wire of radius 15 cm. If the magnitude of the

magnetic field changes from 3.6 T to 5.8 T in 0.18 s, what is the average induced voltage in the loop?

Answer:

The area of the loop isA=πr^2 =π( 1. 5 × 10 −^1 m)^2 = 0. 0707 → 0. 071 m^2.

Since the magnetic field lines pass perpendicularly though the loop, the angle between the area vector and the

magnetic field is zero degrees. Thus,

Φ=BAcos 0◦=BA.

The induced voltage is thereforeV=−N∆(∆BAt)=−∆(∆BAt), since there is only one loop(N= 1 ).

According to the problem, the magnet field changes, but the area of the loop remains constant

V=−A∆∆Bt =−( 0. 707 m^2 )

( 5. 8 T− 3. 6 T

0. 18 s

)

=− 8. 64 →− 8. 6 V.

The negative sign indicates that the induced voltage produces a current whose magnetic field opposes the direction

of the original change in magnetic flux.

b. If the resistance of the loop is 16Ω, what is the induced current in the loop?

Answer:Using Ohm’s law,I=VR=^816.^64 = 0. 54 A.