Question

A circular coil of diameter$21cm$ is placed in a magnetic field of induction${10}^{-4}T$. The magnitude of flux linked with the coil, when the plane of coil makes an angle$30°$ with the field is

• A. $1.44x{10}^{-6}Wb$
• B. $1.732x{10}^{-6}Wb$
• C. $3.1x{10}^{-6}Wb$
• D. $4.2x{10}^{-6}Wb$

Answer 1

The correct option is B

$1.732x{10}^{-6}Wb$

Step 1 : Given data

Diameter of coil $$\begin{gathered} D=21cm \\ =0.21m \end{gathered}$$

Magnetic field $B={10}^{-4}T$

Angle between $\overrightarrow{B}\&\overrightarrow{A}=\theta ={60}^0$

Where $\overrightarrow{A}$$=$Area vector of coil

Step 2: To find the value of magnetic flux

We know that magnetic flux $\varphi =\overrightarrow{B}.\overrightarrow{A}=BA\cos \theta$

$$\begin{gathered} \varphi ={10}^{-4}\left(\frac{\pi }{4}\times D^2\right)\times \cos 60 \\ ={10}^{-4}\times \frac{\pi }{4}\times {\left(0.21\right)}^2\times \frac{1}{2} \\ =\frac{21\times 21\pi }{8}\times {10}^{-8}=173.09\times {10}^{-8} \\ \varphi =1.73\times {10}^{-6}Wb \end{gathered}$$

Hence the magnetic flux $\varphi =1.73\times {10}^{-6}Wb$

So the correct answer is Option B