Q8 of 104 Page 306

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.



Given:


Area of conducting loop=


Variation of magnetic field with time


Angle of field with normal to coil θ =60°


Magnetic flux due to magnetic field B through cross section area A is given by



Here flux through the loop is given by


. (i)


Also,


by faraday’s law of electromagnetic induction



Where


ϵ =emf produced


ϕ =flux of magnetic field


using eqn.(i)


we get


…(ii)


Since maximum value of cosωt =1


Therefore, maximum value of magnitude of emf induced in the loop is given by



Putting the values of B0 and ω we get,



Therefore, maximum value of emf induced in the coil is 0.015V


(b) from eqn.(ii), we have



At t=π/900 s magnitude of induced emf is given by



Therefore magnitude of induced emf at t=π/900 is


(c) from eqn.(ii), we have



At t=π/600 s magnitude of induced emf is given by



Therefore magnitude of induced emf at t=π/600 is


More from this chapter

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6

A square-shaped copper coil has edges of length 50 cm and contains 50 turns. It is placed perpendicular to a 1.0T magnetic field. It is removed from the magnetic field in 0.25 s and restored in its original place in the next 0.25 s. Find the magnitude of the average emf induced in the loop during

(a) its removal, (b) its restoration and (c) its motion.


 7

Suppose the resistance of the coil in the previous problem is 25 Ω. Assume that the coil moves with uniform velocity during its removal and restoration. Find the thermal energy developed in the coil during

(a) its removal


(b) its restoration and


(c) its motion.


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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?


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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