Question

# An induced e.m.f. is produced when a magnet is plunged into a coil. The strength of the induced current is independent of

A
the strength of the magnet
B
number of turns of coil
C
the resistivity of the wire of the coil
D
size of the magnet

Solution

## The correct option is D size of the magnetAn induced e.m.f is produced when a magnet is plunged into a coil. This is because of the rate of change of flux, which induces e.m.f. i.e.$$\epsilon =\dfrac { dQ }{ dt } =\dfrac { d }{ dt } (nBA)\quad \quad \quad \quad \quad \quad as\quad Q=nBA$$where     $$\epsilon$$ = e.m.f. inducedQ = flux linked (variable)n= number of turns of coilB=magnetic field strength A= area of cross section of the coilso now if the resistance of the coli is R (let)then induced current = i=$$\dfrac { \varepsilon }{ R } \quad =\dfrac { 1 }{ R } \dfrac { d }{ dt } (nBA)=\dfrac { n }{ R } \dfrac { d }{ dt } (\vec B.\vec A)$$    $$\rightarrow$$ 1From ths equation it's clear that current depends on strength of the magnet (B), number of turns of the coil (n) and resistivity of the wire but it doesn't depend upon the size of the magnet.Physics

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