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
Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it.
What is the direction of induced currents in metal rings 1 and 2 when current I in the wire is increasing steadily?
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.
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 short magnet is moved along the axis of a conducting loop. Show that the loop repels the magnet if the magnet is approaching the loop and attracts the magnet if it is going away from the loop.
The battery discussed in the previous question is suddenly disconnected. Is a current induced in the other loop? If yes, when does it start and when does it end? Do the loops attract each other or repel?
A bar magnet is released from rest along the axis of a very long, vertical copper tube. After some time the magnet ____________ .
Consider the situation shown in figure. If the closed loop is completely enclosed in the circuit containing the switch, the closed loop will show _______________ .
Which of the following statements is not correct?
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 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.
Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current I (Figure). The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off, what will happen to the ring?
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.
Predict the direction of induced current in the situation described by the following figure.
