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An air-cored solenoid with length 30 cm, area of cross-section `25 cm^(2)` and number of turus 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 magnetie field near the ends of the solenoid. |
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Answer» Given, length of solenoid `l=30" cm "30 xx 10^(-2)m` Area of cross-section `A=25"cm "25 xx 10^(-4)m^(2)` Number of turns N=500, Current `I_1=2.5A, I_(2)=0`, Brief time `dt=10^(-3)s`. Induced emf in the solenoid `e=(dphi)/(dt)=(d(BA))/(dt) (therefore phi=BA)` Magnetic field induction B at a point well inside the long solenoid carrying cuurent I is `B=mu_(0)nI("where, n"=N/l)` `e=NA (dB)/(dt)=A(d)/(dt)(mu_(0)N/l.I)` `e=A(m_(0)N)/(l).(dI)/(dt)` `e=500xx25xx10^(-4)xx4xx3.14xx10^(-7) xx (500)/(30xx10^(-2))xx(2.5)/(10^(-3)) Rightarrow e=6.5V` |
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