Question
Hard
Solving time: 5 mins
Q.206. A current flowing in the winding of a long straight solenoid is increased at a sufficiently slow rate. Demonstrate that the rate at which the energy of the magnetic field in the solenoid increases is equal to the flux of the Poynting vector across the lateral surface of the solenoid.
Text solutionVerified
Within the solenoid and the rate of change of magnetic energy
where R = radius of cross-section of the solenoid length.
Also along the axis within the solenoid.
By Faraday’s law, the induced electric field is
or,
so at the edge (circuital)
Then and
(radially inward)
as before.
where R = radius of cross-section of the solenoid length.
Also along the axis within the solenoid.
By Faraday’s law, the induced electric field is
or,
so at the edge (circuital)
Then and
(radially inward)
as before.
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Question Text | Q.206. A current flowing in the winding of a long straight solenoid is increased at a sufficiently slow rate. Demonstrate that the rate at which the energy of the magnetic field in the solenoid increases is equal to the flux of the Poynting vector across the lateral surface of the solenoid. |
Topic | Electromagnetic Waves |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 35 |