Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Predict the direction of induced current in the situation described by the following figure.
Predict the direction of induced current in metal rings 1 and 2 when current I in the wire is steadily decreasing?
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 pivoted aluminium bar falls much more slowly through a small region containing a magnetic field than a similar bar of an insulating material. Explain.
A bar magnet is released from rest along the axis of a very long, vertical copper tube. After some time the magnet ____________ .
Two circular loops of equal radii are placed coaxially at some separation. The first is cut and a battery is inserted in between to drive a current in it. The current changes slightly because of the variation in resistance with temperature. During this period, the two loops _______________ .
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.
A bar magnet is dropped through a copper ring acceleration of magnet is
For a coil having L = 2 mH, current flows at the rate of 10-3 AIS. The e.m.f induced is
There are two coils A and B as shown in figure. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that ______.
Consider a magnet surrounded by a wire with an on/off switch S (Figure). If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? 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.
Consider a metal ring kept on top of a fixed solenoid (say on a carboard) (Figure). The centre of the ring coincides with the axis of the solenoid. If the current is suddenly switched on, the metal ring jumps up. 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.
