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प्रश्न
Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current through it grows from zero to ‘I’.
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उत्तर
When the current is varied, the flux linked with the coil changes and an e.m.f. is induced in the coil. It is given as
`in=-(d(Nphi_E))/dt=-L(dI)/dt`
The self-induced e.m.f. is also called back e.m.f. as it opposes any change in current in the circuit. So, work needs to be done against back e.m.f. in establishing current.
This work done is stored as magnetic potential energy.
The rate of doing work is given as
`(dW)/(dt)=|in|I=LI(dI)/dt " (neglecting negative sign)"`
Thus, the total work done in establishing current from 0 to I is
`w=intdw=int_0^1LIdI=1/2LI^2`
संबंधित प्रश्न
Define the term self-inductance of a solenoid.
A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5 A is held directly above AB at a height of 1 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms−2]
A wire AB is carrying a steady current of 10 A and is lying on the table. Another wire CD carrying 6 A is held directly above AB at a height of 2 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms−2]
Draw and compare the pattern of the magnetic field lines in the two cases ?
How is the magnetic field inside a given solenoid made strong?
The magnetic field B inside a long solenoid, carrying a current of 5.00 A, is 3.14 × 10−2 T. Find the number of turns per unit length of the solenoid.
A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1.0 × 10−2 T near the centre of the solenoid.
A tightly-wound, long solenoid carries a current of 2.00 A. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of 1.00 × 108 rev s−1. Find the number of turns per metre in the solenoid.
A current of 1.0 A is established in a tightly wound solenoid of radius 2 cm having 1000 turns/metre. Find the magnetic energy stored in each metre of the solenoid.
