Question

If the flux of magnetic induction through a coil of resistance R and having n turns changes from ${\Phi }_1$ to ${\Phi }_2$, then the magnitude of the charge that passes through the coil is

• A. $\frac{{\Phi }_2-{\Phi }_1}{R}$
• B. $n\frac{{\Phi }_2-{\Phi }_1}{R}$
• C. $\frac{{\Phi }_2-{\Phi }_1}{nR}$
• D. $\frac{nR}{{\Phi }_2-{\Phi }_1}$

Answer 1

The correct option is B

$n\frac{{\Phi }_2-{\Phi }_1}{R}$

Induced emf is $|e|=n\frac{\Delta \Phi }{\Delta t}$, Now
$\Delta q=1\Delta t=\frac{e}{R}\Delta t=\frac{n\Delta \Phi }{R\Delta t}\times \Delta t=\frac{n\Delta \Phi }{R}=\frac{n({\Phi }_2-{\Phi }_1)}{R}$