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
Consider two nested, spherical conducting shells shown in grey and red in the figure 7. The first
has inner radius a and outer radius b. The second has inner radius c and outer radius d.
Case I A positive charge +Q is introduced into the center of the inner spherical shell (the grey
shell).
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
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