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Question

The Poynting Vector in an RL Circuit An RL circuit consists of an ideal battery of voltage V, a switch S, a resistor R, and a solenoid inductor of radius R and length L with n loops per unit length as shown. The switch is closed at time t. What is the voltage across the inductor, Vi(t), as a function of time? What is the magnitude of the magnetic field inside the solenoid inductor, B(t)? (Neglect edge effects.) What is the energy of the magnetic field, UB, stored in the cylindrical volume of the inductor? Is this energy increasing or decreasing? What is the rate of change of energy, dUB/dt? What is the electric field, El(t), inside the inductor at a distance r from the axis of the solenoid? Here you will need to use Faraday's Law in the language of Maxwell's equations: the change in magnetic flux produces a circular electric field. How are B and E oriented? How is the Poynting vector, S, oriented? What is the magnitude of the Poynting vector, S(r,t), at the edge of the volume of the inductor? What is the value of the integral of S(r,t) Â· dA over the cylindrical surface that encloses the volume of the inductor? This is the total flux out of the cylinder (it may be negative). How does S(r,t) Â· dA compare to dUB/dt that you computed above? What is the relationship?

          The Poynting Vector in an RL Circuit

An RL circuit consists of an ideal battery of voltage V, a switch S, a resistor R, and a solenoid inductor of radius R and length L with n loops per unit length as shown. The switch is closed at time t.

What is the voltage across the inductor, Vi(t), as a function of time? What is the magnitude of the magnetic field inside the solenoid inductor, B(t)? (Neglect edge effects.) What is the energy of the magnetic field, UB, stored in the cylindrical volume of the inductor? Is this energy increasing or decreasing? What is the rate of change of energy, dUB/dt? What is the electric field, El(t), inside the inductor at a distance r from the axis of the solenoid? Here you will need to use Faraday's Law in the language of Maxwell's equations: the change in magnetic flux produces a circular electric field. How are B and E oriented? How is the Poynting vector, S, oriented? What is the magnitude of the Poynting vector, S(r,t), at the edge of the volume of the inductor? What is the value of the integral of S(r,t) Â· dA over the cylindrical surface that encloses the volume of the inductor? This is the total flux out of the cylinder (it may be negative). How does S(r,t) Â· dA compare to dUB/dt that you computed above? What is the relationship?

the poynting vector in an rl circuit direction elrt srt an rl circuit consists of an ideal battery of voltage v switch resistor r ad solenoid indluctor ol radius fo length andl loops per 33113

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