Question

A coil of mean area $500c{m}^2$ and having $1000$ turns is held perpendicular to a uniform field of $0.4$ gauss The coil is turned through $180^{\circ }$ in $\frac{1}{10}$ second. The average induced emf is

• A. $0.02V$
• B. $0.04V$
• C. $1.4V$
• D. $0.08V$

Answer 1

Answer: (B)

Here, $A=500c{m}^2=500\times 10^{-4}{m}^2$
$N=1000,B=0.4G=0.4\times 10^{-4}T$
$t=\frac{1}{10}s$
When the coil is held perpendicular to the field, the normal to the plane of the coil makes an angle of $0^{\circ }$ with the field $B$.
$\therefore$ initial flux, ${\varphi }_1=BAcos{0}^{\circ }=BA$
final flux, ${\varphi }_2=BAcos180^{\circ }=-BA$
$\epsilon =-N(\frac{({\varphi }_2-{\varphi }_1)}{t})=-N(\frac{-BA-BA}{t})$
$=\frac{2NBA}{t}$
$=\frac{2\times 1000\times 0.4\times 10^{-}4\times 500\times 10^{-4}}{1/10}$
$=0.04V$