The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius r inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b) Find the magnitude of the induced electric field inside the solenoid, at a distance r¡ from its axis. Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric field outside the solenoid, at a distance r, from the axis? (d) Graph the magnitude of the induced electric field as a function of the distance r from the axis from r = 0 to r = 2R. (e) What is the magnitude of the induced emf in a circular turn of radius R/2 that has its center on the solenoid axis? (f) What is the magnitude of the induced emf if the radius in part (e) is R? (g) What is the induced emf if the radius in part (e) is 2R?

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Please answer part f and  g  showing all the steps with detailed explanation

The magnetic field within a long, straight solenoid with a circular cross section and radius R is
increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius ri
inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b)
Find the magnitude of the induced electric field inside the solenoid, at a distance rị from its axis.
Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric
field outside the solenoid, at a distance r, from the axis? (d) Graph the magnitude of the induced
electric field as a function of the distance r from the axis from r = 0 to r = 2R. (e) What is the
magnitude of the induced emf in a circular turn of radius R/2 that has its center on the solenoid
axis? (f) What is the magnitude of the induced emf if the radius in part (e) is R? (g) What is the
induced emf if the radius in part (e) is 2R?
Transcribed Image Text:The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius ri inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b) Find the magnitude of the induced electric field inside the solenoid, at a distance rị from its axis. Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric field outside the solenoid, at a distance r, from the axis? (d) Graph the magnitude of the induced electric field as a function of the distance r from the axis from r = 0 to r = 2R. (e) What is the magnitude of the induced emf in a circular turn of radius R/2 that has its center on the solenoid axis? (f) What is the magnitude of the induced emf if the radius in part (e) is R? (g) What is the induced emf if the radius in part (e) is 2R?
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