Question

A coil mean area 500 $c{m}^2$ and having $1000$ turns is held perpendicular to a uniform field of $0.4$ gauss. The coil is turned through ${180}^0$ 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)

$0.04V$

Here $A=500c{m}^{=}500\times {10}^{-4}{m}^2$
N=1000, B=0.4, $G=0.4\times {10}^{-4}T$
$t=\frac{1}{10}s$

When the coil is held perpenducular to the field, the normal to the plane of the coil makes an angle of $0^o$ with the field B.
$\therefore$ initial flux ${\varphi }_1=BAcos{0}^o=BA$
Final flux ${\varphi }_2=BAcos{180}^o=-BA$ Average induced emf,
$ϵ=-Nd\left(\frac{{\varphi }_2-{\varphi }_1}{t}N\right)$
$=-N\left(\frac{-BA-BA}{t}\right)$
$\frac{2NBA}{t}=\frac{2\times 1000\times 0.4\times {10}^{-4}\times 500\times {10}^{-4}}{1/10}=0.04V$