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Consider the self-inductance per unit length of a solenoid at its centre and that near its ends. Which of the two is greater?
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A constant current i is maintained in a solenoid. Which of the following quantities will increase if an iron rod is inserted in the solenoid along its axis?
(a) magnetic field at the centre
(b) magnetic flux linked with the solenoid
(c) self-inductance of the solenoid
(d) rate of Joule heating.
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Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current goes through them
(d) time constant if one solenoid is connected to one battery and the other is connected to another battery.
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Consider the situation described in the previous problem. Suppose the current i enters the loop at the points A and leaves it at the point B. Find the magnetic field at the centre of the loop.
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Find the thermo-emf developed in a copper-silver thermocouple when the junctions are kept at 0°C and 40°C. Use the data given in the following table.
| Metal with lead (Pb) |
a `mu V"/"^oC` |
b `muV"/("^oC)` |
| Aluminium | -0.47 | 0.003 |
| Bismuth | -43.7 | -0.47 |
| Copper | 2.76 | 0.012 |
| Gold | 2.90 | 0.0093 |
| Iron | 16.6 | -0.030 |
| Nickel | 19.1 | -0.030 |
| Platinum | -1.79 | -0.035 |
| Silver | 2.50 | 0.012 |
| Steel | 10.8 | -0.016 |
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Find the neutral temperature and inversion temperature of a copper-iron thermocouple if the reference junction is kept at 0°C. Use the data given in the following table.
| Metal with lead (Pb) |
a `mu V"/"^oC` |
b `muV"/("^oC)` |
| Aluminium | -0.47 | 0.003 |
| Bismuth | -43.7 | -0.47 |
| Copper | 2.76 | 0.012 |
| Gold | 2.90 | 0.0093 |
| Iron | 16.6 | -0.030 |
| Nickel | 19.1 | -0.030 |
| Platinum | -1.79 | -0.035 |
| Silver | 2.50 | 0.012 |
| Steel | 10.8 | -0.016 |
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A thin but long, hollow, cylindrical tube of radius r carries i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube (b) outside the tube.
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A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnitude filed at a point (a) just inside the tube (b) just outside the tube.
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A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.
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A solid wire of radius 10 cm carries a current of 5.0 A distributed uniformly over its cross section. Find the magnetic field B at a point at a distance (a) 2 cm (b) 10 cm and (c) 20 cm away from the axis. Sketch a graph B versus x for 0 < x < 20 cm.
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Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.
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Two large metal sheets carry currents as shown in figure. The current through a strip of width dl is Kdl where K is a constant. Find the magnetic field at the points P, Q and R.
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Consider the situation of the previous problem. A particle having charge q and mass mis projected from the point Q in a direction going into the plane of the diagram. It is found to describe a circle of radius r between the two plates. Find the speed of the charged particle.
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An average emf of 20 V is induced in an inductor when the current in it is changed from 2.5 A in one direction to the same value in the opposite direction in 0.1 s. Find the self-inductance of the inductor.
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A magnetic flux of 8 × 10−4 weber is linked with each turn of a 200-turn coil when there is an electric current of 4 A in it. Calculate the self-inductance of the coil.
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An inductor-coil carries a steady-state current of 2.0 A when connected across an ideal battery of emf 4.0 V. If its inductance is 1.0 H, find the time constant of the circuit.
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When an electron strikes the target in a Coolidge tube, its entire kinetic energy
(a) is converted into a photon
(b) may be converted into a photon
(c) is converted into heat
(d) may be converted into heat.
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A coil having inductance 2.0 H and resistance 20 Ω is connected to a battery of emf 4.0 V. Find (a) the current at the instant 0.20 s after the connection is made and (b) the magnetic field energy at this instant.
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An inductor of inductance 5.0 H, having a negligible resistance, is connected in series with a 100 Ω resistor and a battery of emf 2.0 V. Find the potential difference across the resistor 20 ms after the circuit is switched on.
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What are the values of the self-induced emf in the circuit of the previous problem at the times indicated therein?
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