Advertisements
Advertisements
प्रश्न
A long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the centre of this coil we place a smaller coil of ‘N’ turns and diameter ‘b’ (where b < a). If the current in the solenoid increases linearly, with time, what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of mt2 + C.
Advertisements
उत्तर
Magnetic field due to a solenoid is given by, B = μ0ni where signs are as usual.
In this problem, the current is varying with time. Due to this an emf is induced in the coil of radius b.
`B_1(t) = mu_0nI(t)`
This varying magnetic field changes flux in the smaller coil.
Magnetic flux in IInd coil
`phi_2 = B(t).A`
= `mu_0nI(t).pib^2`
Induced e.m.f in second coil due to solenoid's varying magnetic field in 1 turn
`ε^' = (-dphi_2)/(dt) = (-d)/(dt) mu_0npib^2I(t)`
= `- mu_0npib^2 d/(dt) (mt^2 + C)`
= `- mu_0npib^2. 2mt`
So net e.m.f. produced in N turns of smaller coil
| ε = `- mu_0Nn pi b^2 2mt` |
APPEARS IN
संबंधित प्रश्न
Predict the direction of induced current in the situation described by the following figure.
Use Lenz’s law to determine the direction of induced current in the situation described by the figure:
A wire of irregular shape turning into a circular shape.
What is the direction of induced currents in metal rings 1 and 2 when current I in the wire is increasing steadily?
Show that Lenz's law is a consequence of conservation of energy.
Predict the directions of induced currents in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing steadily.
A bar magnet is moved in the direction indicated by the arrow between two coils PQ and CD. Predict the directions of induced current in each coil.
A bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet, an anticlockwise current is found to be induced in the ring. Which of the following may be true?
(a) The south pole faces the ring and the magnet moves towards it.
(b) The north pole faces the ring and the magnet moves towards it.
(c) The south pole faces the ring and the magnet moves away from it.
(d) The north pole faces the ring and the magnet moves away from it.
Explain, with the help of a suitable example, how we can show that Lenz's law is a consequence of the principle of conservation of energy.
2 A 40 kg boy whose legs are 4 cm in area and 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can withstand stress of 0.9 x 108 N/m2. The Young's modulus for the material of the bone is ______.
Energy dissipate in LCR circuit in
Same as problem 4 except the coil A is made to rotate about a vertical axis (figure). No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this instant, t = 0, is ______.
A wire in the form of a tightly wound solenoid is connected to a DC source, and carries a current. If the coil is stretched so that there are gaps between successive elements of the spiral coil, will the current increase or decrease? Explain.
A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.
A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating: It is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to:
Predict the direction of induced current in the situation described by the following figure.
Predict the direction of induced current in the situation described by the following figure.
Predict the direction of induced current in the situation described by the following figure.
In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:
In the diagram given below, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:
