Q10 of 104 Page 306

A conducting square loop having edges of length 2.0 cm is rotated through 180° about a diagonal in 0.20 s. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is 20 mV, find the magnitude of the magnetic field


Given:


Average induced emf in the loop


Time taken to rotate the loo


Edge length of square loop


Area of square loop


We know that,


Average induced emf in time interval Δt is given by


…(i)


Where


are flux across the cross section at time intervals respectively.


Magnetic flux(ϕ) through the loop is given by the formula




Where B=magnetic field intensity


A=area of cross section


θ =angle between area vector and magnetic field


Initially, angle between area vector and magnetic field is 0°


Therefore, initial flux through the coil is



When it is rotated by 180° flux passing through the coil is given by



Putting this values in eqn.(i) we get,



Putting the values of ϵ, B and Δt in the above eqn.




Therefore, magnitude of magnetic field intensity is 5T


More from this chapter

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8

A conducting loop of area 5.0 cm2 is placed in a magnetic field which varies sinusoidally with time as B = B0 sin ωt where B0 = 0.20 T and ω = 300 s–1. The normal to the coil makes an angle of 60° with the field. Find

(a) the maximum emf induced in the coil,


(b) the emf induced at τ = (π/900) s and


(c) the emf induced at t = (π/600) s.


 9

Figure shows a conducting square loop placed parallel to the pole-faces of a ring magnet. The pole-faces have an area of 1 cm2 each and the field between the poles is 0.10 T. The wires making the loop are all outside the magnetic field. If the magnet is removed in 1.0 s, what is the average emf induced in the loop?


 11

A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field. Find the charge which flows through any cross-section of the wire in the process. Note that it is independent of the shape of the loop as well as the way it is withdrawn.

 12

A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of 20 Ω is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.