Question

A loop ABCD have current i = 10 A as shown in the figure. AB and CD are of radius 3cm and 5cm Respectively determine magnetic field intensity at O.

• A. $\frac{200\pi }{3}\times {10}^{-7}T$
• B. $\frac{100\pi }{3}\times {10}^{-7}T$
• C. $100\pi \times {10}^{-7}T$
• D. $200\pi \times {10}^{-7}T$

Answer 1

The correct option is B $\frac{100\pi }{3}\times {10}^{-7}T$

$\text{Given:-}$Radius of arc

QR = 3cm =$r_1$

PS = 5cm =$r_2$

$\text{To find:-}$Determine magnetic field intensity at O.

$\text{Solution:-}$

Magnetic field due to an an arc = $\frac{M_{O}I}{4\pi r}\theta$

So,Magnetic field at O

$B_{QR}-B_{PS}$ (Since current is in opposite direction )

$\Rightarrow \frac{M_{O}I}{4\pi }\theta [\frac{1}{3}-\frac{1}{5}]\times \frac{1}{{10}^{-2}}$

$=\frac{4\pi \times {10}^{-7}\times 10}{4\pi }\times \frac{\pi }{4}\times \frac{2}{15}\times {10}^2$

$=\frac{100\pi }{3}\times {10}^{-7}T$

$\text{Hence the correct option is B}$