College Physics
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To explain self-inductance, it is helpful to consider the specific example of a long solenoid, as shown in the figure. This solenoid has only one winding, and so the EMF induced by its changing current appears across the solenoid itself. This contrasts with mutual inductance, where this voltage appears across a second coil wound on the same cylinder as the first.
Assume that the solenoid has radius R, length Z along the z axis, and is wound with nnn turns per unit length so that the total number of turns is equal to nZ. Assume that the solenoid is much longer than its radius.
A.
Suppose that the current varies with time, so that dI(t)/dt≠0. Find the electromotive force EMF induced across the entire solenoid due to the change in current through the entire solenoid.
Express your answer in terms of dI(t)/dt, n, Z, and R.
B.
The self-inductance L is related to the self-induced EMF E(t)by the equation E(t)=−LdI(t)/dtt. Find L for a long solenoid. (Hint: The self-inductance L will always be a positive quantity.)
Express the self-inductance in terms of the number of turns per length n, the physical dimensions R and Z, and relevant constants.
Transcribed Image Text:Learning Goal:
To explain self-inductance, it is helpful to consider the
specific example of a long solenoid, as shown in the
figure. This solenoid has only one winding, and so the
EMF induced by its changing current appears across the
solenoid itself. This contrasts with mutual inductance,
where this voltage appears across a second coil wound
on the same cylinder as the first.
(Figure 1)
Assume that the solenoid has radius R, length Z along
the z axis, and is wound with n turns per unit length so
that the total number of turns is equal to nZ. Assume
that the solenoid is much longer than its radius.
Figure
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Suppose that the current varies with time, so that di (t)/dt = 0. Find the electromotive force & induced
across the entire solenoid due to the change in current through the entire solenoid.
Express your answer in terms of dI (t)/dt, n, Z, and R.
► View Available Hint(s)
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Transcribed Image Text:Learning Goal:
To explain self-inductance, it is helpful to consider the
specific example of a long solenoid, as shown in the
figure. This solenoid has only one winding, and so the
EMF induced by its changing current appears across the
solenoid itself. This contrasts with mutual inductance,
where this voltage appears across a second coil wound
on the same cylinder as the first.
(Figure 1)
Assume that the solenoid has radius R, length Z along
the z axis, and is wound with n turns per unit length so
that the total number of turns is equal to nZ. Assume
that the solenoid is much longer than its radius.
Figure
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Air-Core Solenoid
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Schematic Symbol
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The self-inductance L is related to the self-induced EMF & (t) by the equation &(t) = −LdI(t)/dt. Find L
for a long solenoid. (Hint: The self-inductance I will always be a positive quantity.)
Express the self-inductance in terms of the number of turns per length n, the physical dimensions R
and Z, and relevant constants.
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