ε = - (BA cos 0) dt ε = -- () (MONA) 71 dI -(-) (MORA) dt = Note that the area A is interpreted as the area A we have MONIA dI dt = -0.500(4 x 10-7 T. m/A) ( 955 -(- Cos 0°) x 10-4 V. Bsolenoid 127 2 of the solenoid, where the field is strong. Substituting, x 10-4 T + m²/s) 1.N-S-¹V-C) c.m.T) ( ₂ turns/m) ( T m)² (270 A/

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E
d
-(BA cos 0) =
dt
dI
= -(-²) (HONA) I
кноп dt
ε = -(²-) (μ₁NA) DI
dt
d
dt
2
Note that the area A is interpreted as the area A = ₂² of the solenoid, where the field is strong. Substituting,
we have
II
(MonIA cos 0°)
HONIA
= −0.500(4 × 10¯7 T · m/A) (1
= (-
955
x 10-4 V.
V. C
x 10−4 T · m²/s)( 1. N. 5) (1¹.
C.m. T
• m
Bsolenoid
turns/m) (
IST
m)² (271
2
Transcribed Image Text:E d -(BA cos 0) = dt dI = -(-²) (HONA) I кноп dt ε = -(²-) (μ₁NA) DI dt d dt 2 Note that the area A is interpreted as the area A = ₂² of the solenoid, where the field is strong. Substituting, we have II (MonIA cos 0°) HONIA = −0.500(4 × 10¯7 T · m/A) (1 = (- 955 x 10-4 V. V. C x 10−4 T · m²/s)( 1. N. 5) (1¹. C.m. T • m Bsolenoid turns/m) ( IST m)² (271 2
=
=
An aluminum ring of radius ₁ 5.00 cm and a resistance of 2.50 × 10-4 is placed around one end of a long
air-core solenoid with 955 turns per meter and radius 2 3.00 cm as shown in the figure below. Assume the
axial component of the field produced by the solenoid is one-half as strong over the area of the end of the
solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-
sectional area. The current in the solenoid is increasing at a rate of 270 A/s.
↑
71
(a) What is the induced current in the ring?
(b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current
in the ring?
(c) At the center of the ring, what is the direction of the magnetic field produced by the induced current
in the ring?
Transcribed Image Text:= = An aluminum ring of radius ₁ 5.00 cm and a resistance of 2.50 × 10-4 is placed around one end of a long air-core solenoid with 955 turns per meter and radius 2 3.00 cm as shown in the figure below. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross- sectional area. The current in the solenoid is increasing at a rate of 270 A/s. ↑ 71 (a) What is the induced current in the ring? (b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring? (c) At the center of the ring, what is the direction of the magnetic field produced by the induced current in the ring?
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