An infinite solenoid with radius a and n turns per unit length carries a current which increases linearly with time, as I(t) = at a > 0. The solenoid is looped by a circular wire of radius r, coaxial with it. The magnetic field due to the current in the solenoid is B = ponI inside the solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note î, 0, and k are the unit vectors, with the axis pointing upward. Use the integral form of Faraday's law, i.e. f E.didto
An infinite solenoid with radius a and n turns per unit length carries a current which increases linearly with time, as I(t) = at a > 0. The solenoid is looped by a circular wire of radius r, coaxial with it. The magnetic field due to the current in the solenoid is B = ponI inside the solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note î, 0, and k are the unit vectors, with the axis pointing upward. Use the integral form of Faraday's law, i.e. f E.didto
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Transcribed Image Text:An infinite solenoid with radius a and n turns per unit length carries a current which increases
linearly with time, as I(t) = at a > 0. The solenoid is looped by a circular wire of radius r,
coaxial with it. The magnetic field due to the current in the solenoid is B = onI inside the
solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note , 0,
and k are the unit vectors, with the z axis pointing upward. Use the integral form of Faraday's
law, i.e. § Ē.dī = – dº to
dt
x
I
Z
↑
0
y
Figure 6: The cylindrical coordinates (r, 0, z) used in question B1
a) Drive an expression for the electric field in the loop for r <a.
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