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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 are the unit vectors, with the z 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 = onI inside the solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note , 0, and are the unit vectors, with the z axis pointing upward. Use the integral form of Faraday's law, i.e. f E.didto

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Consider two nested, spherical conducting shells shown in grey and red in the figure 7. The first
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Asnwer a-cAn infinite solenoid with radius a and n turns per unit length carries a current which increases
linearly with time, as I(t) = αt α > 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 = µ0nI inside the
solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, θ, z) and note rˆ,
ˆθ,
and ˆk are the unit vectors, with the z axis pointing upward. Use the integral form of Faraday’s
law, i.e. H
E.d ⃗ ⃗l = −
dϕ
dt to

Answer a-c

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 = on I inside the solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note , ê, and are the unit vectors, with the z axis pointing upward. Use the integral form of Faraday's law, i.e. f E.didto I Z A ∙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. b) Drive an expression for the electric field in the loop for r > a. c) Verify that your result satisfies the local form of the law, × E = - 0B Ət d) Explain the direction of the flowing induced current in the loop. No calculation needed. e) Copy the drawing in your submission and indicate the direction of the magnetic field, electric field and induced current.
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 = on I inside the solenoid and B = 0 outside the solenoid. Use the cylindrical coordinates (r, 0, z) and note , ê, and are the unit vectors, with the z axis pointing upward. Use the integral form of Faraday's law, i.e. f E.didto I Z A ∙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. b) Drive an expression for the electric field in the loop for r > a. c) Verify that your result satisfies the local form of the law, × E = - 0B Ət d) Explain the direction of the flowing induced current in the loop. No calculation needed. e) Copy the drawing in your submission and indicate the direction of the magnetic field, electric field and induced current.
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