PredictthedirectionofinducedcurrentinthesituationsdescribedbythefollowingFigs. 6.18(a) to (f ). (a) (b) (c) (d) (e) (f)

A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s^-1 about an axisnormaltotherodpassingthroughitsoneend.Theotherendoftherodisincontact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.

A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s^-1 in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^-1 in a uniform horizontal magnetic field of magnitude 3.0×10^-2 T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10?, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s^-1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10^-4 Wb m^-2. (I) What is the instantaneous value of the emf induced in thewire? (II) What is the direction of theemf? (III) Which end of the wire is at the higher electrical potential?

Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10^-4 T and the dip angle is 30°.

Suppose the loop in Exercise 6.4 is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s^-1. If the cut is joined and the loop has a resistance of 1.6 ? how much power is dissipated by the loop as heat? What is the source of this power?

A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s^-1 in the positive x-direction in an environment containing a magnetic fieldinthepositivez-direction.Thefieldisneitheruniforminspacenorconstantintime. It has a gradient of 10^-3 T cm^-1 along the negative x-direction (that is it increases by 10^-3 T cm^-1 as one moves in the negative x-direction), and it is decreasing in time at the rate of 10^-3 T s^-1. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50m?.

It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm² with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 ?. Estimate the field strength of magnet.

Figure 6.20 shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 m?. Assume the field to be uniform. (I) SupposeKisopenandtherodismovedwithaspeedof12cms^-1inthedirection shown. Give the polarity and magnitude of the inducedemf. (II) Isthereanexcesschargebuiltupattheendsoftherodswhen K is open? What if K is closed? (III) With K open and the rod moving uniformly, there is no net force on the electrons in therodPQeventhoughtheydoexperiencemagneticforceduetothemotionoftherod. Explain. (IV) What is the retarding force on the rod when K isclosed? (V) Howmuchpowerisrequired(byanexternalagent)tokeeptherodmovingatthe same speed (=12 cm s^-1) when K is closed? How much power is required when K is open? (VI) How much power is dissipated as heat in the closedcircuit? What is the source of this power? (VII) Whatistheinducedemfinthemovingrodifthemagneticfieldisparalleltotherails instead of beingperpendicular?

An air-cored solenoid with length 30 cm, area of cross-section 25 cm² and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10^-3 s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

(I) Obtainanexpressionforthemutualinductancebetweenalongstraightwireanda square loop of side a as shown in Fig.6.21. (II) Nowassumethatthestraightwirecarriesacurrentof50 Aandtheloopismovedto the right with a constant velocity, v = 10m/s. Calculate the induced emf in the loop at the instant when x = 0.2 m. Take a = 0.1 m and assume that the loop has a large resistance.

A line charge ? per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Fig. 6.22). A uniform magnetic field extends over a circular region within the rim. It is given by, B = - B₀ k (r = a; a < R) = 0 (otherwise) What is the angular velocity of the wheel after the field is suddenly switched off?