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Magnetic flux phi_(B) through a plane of area 'A' placed in a uniform magnetic field vceB is given as: phi_(B)= vceB.vceA = BA cos theta where theta is the angle between vceB and vceA. The above relatio can be extended to curved surfaces and non-uniform fields. In general, if the magnetic field has different magnitudes an directions at various parts of a surface, then the magnetic flux through the surface is given by phi_(B)=int vec B.dvecA On the basis of the experimental observations, Faraday concluded that an emf is induced in a coil when magnetic flux through the coil changes with time. Faraday stated his conclusions in the form of a law called Faraday's law of electromagnetic induction. As per this law, the induced emf is given by varepsilon = -(dphi_(B))/dt The negative sign in the expression indicates the direction of induced emfe and hence the direction of current in a closed loop. In the case of a closely would coil of N turns, change of flux associated with each turns is the same and so that total induced emf is given by varepsilon=-N(dphi_(B))/dt From above relations it is clear that the magnetic flux can be changed by changing any one or more of the terms vceB, vceA and theta. (a) Give SI unit of magnetic flux. (b) How is it related to tesla ? (c) Obtain dimensional formula of magnetic flux. (d) A loop of area 4 xx 10^(-3)m^(2) is placed with its plane perpendicular to a uniform magnetic field of 0.02 T. If the loop is quickly removed from the magnetic field within a time of 2 ms, what is the magnitude of induced emf across the two ends of the loop ? (e) If the resistance of the loop be 0.2Omega and a sensitive milliammeter be connected between the two ends of loop, what will be the reading of milliammeter? |
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Answer» SOLUTION :(a) SI unit of magnetic FLUX is weber (Wb). (b) `1Wb=1Tm^(2)`, (c) Since `|varepsilon|=phi_(B)/t, "hence" [phi_(B)]=[varepsilon]xx[t]=[ML^(2)T^(-3)A^(-1)]xx[T]=[ML^(-2)T^(-2)A^(-1)]` (d) Here `phi_(i) = BA = 0.02 xx 4 xx 10^(-3) = 8 xx 10^(-5) "Wb and" phi_(f)=0` `therefore |varepsilon|=(phi_(i)-phi_(f))/t=(8 xx 10^(-5) -0)/(2XX10^(-3))= 4 xx 10^(-2)V=0.04V` |
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