Question

A closely wound flat circular coil of $25$ turns of wire has diaineter of $10\, cm$ which carries current of $4\, A$, the flux density at the centre of a coil will be

• A. $2.28 \times 10^{-6} T$
• B. $1.679 \times 10^{-6} T$
• C. $1.256 \times 10^{-3} T$
• D. $1.572 \times 10^{-5} T$

Answer 1

The Correct Option is C

Number of turns in the coil, $n=25$ Diameter of coil, $d=10\, cm$ $=0 .1 \,m$ $\therefore$ Radius, $r=\frac{0.1}{2}=0.05\, m$ Current $i=4\, A$ Hence, flux density of the coil at the centre is given by $B=\frac{\mu_{0}}{4 \pi} \times \frac{2 \pi n i}{r}$ $=10^{-7} \times \frac{2 \pi \times 25 \times 4}{0.05}$ $=1.256 \times 10^{-3} T$ $\left(\because \mu_{0}=4 \pi \times 10^{-7} NA ^{-1} m ^{-1}\right)$