Q25 of 32 Page 37

Consider an infinitely long wire carrying a current I(t), with . Find the current produced in the rectangular loop of wire ABCD if its resistance is R (Fig. 6.13).


XY is infinitely long wire carrying I(t) such that

at a distance r from the wire strength of the magnetic field


it is direction is outward of the paper total magnetic flux linked with the rectangular loop



on integrating and applying the limit we get



Where L is the self-inductance of the loop



INDUCED CURRENT



More from this chapter

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23

A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in Fig 6.11. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field .


(i) Write down equation for the acceleration of the wire XY.


(ii) If B is independent of time, obtain v(t), assuming v (0) = u0.


(iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.


 24

ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) and OP is a conductor which rotates clockwise with an angular velocity (Fig 6.12). The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in electric contact with ABDC. The rotating conductor has a resistance of λ per unit length. Find the current in the rotating conductor, as it rotates by 180°.


 26

A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current for 0 ≤ t ≤ T and I (0) = 0 for t > T (Fig. 6.14). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.


 27

A magnetic field B is confined to a region r ≤ a and points out of the paper (the z-axis), r = 0 being the center of the circular region. A charged ring (charge = Q) of radius b, b >a and mass m lies in the x-y plane with its center at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time Δt. Find the angular velocity of the ring after the field vanishes.