The magnetic field inside a -diameter superconducting solenoid varies sinusoidally between and at a frequency of .
a. What is the maximum electric field strength at a point from the solenoid axis?
b. What is the value of B at the instant E reaches its maximum value?
(a) The electric field at above the axis of solenoid is
(b) The value of the instant reaches its maximum is
The solenoid is the current carrying wire. The electric field circles around inside the solenoid.
So at a distance .
When magnetic field varies sinusoidally the expression for magnetic field is.
Substitute for , for and for .
Substitute for for , and for
The electric field will be maximum when
Substitute (to write the above expression in term of).
Substitute for to find .
The electric field reaches maximum when,
Where sine function goes to zero.
So when electric field reaches maximum,
A long, thin superconducting wire carrying a current passes through the center of a thin, -diameter ring. A uniform electric field of increasing strength also passes through the ring, parallel to the wire. The magnetic field through the ring is zero.
. At what rate is the electric field strength increasing?
. Is the electric field in the direction of the current or opposite to the current?
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