Question

A circular coil of diameter 21 cm 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 of $30^o$ with the field is:
(a) $1.44 \times {10^{-6}}~ Wb$
(b) $1.732 \times {10^{-6}}~ Wb$
(c) $3.1 \times {10^{-6}}~ Wb$
(d) $4.2 \times {1^{-6}}~ Wb$

Answer 1

Hint: To solve this question will use the concept of flux and magnetic field of induction. When a circular coil carrying electricity is put in an even magnetic field, the torque acting on the coil is not zero, which causes the coil to rotate. To solve this, we will simply use the given values in the formula.

Formula Used:
\[\Phi = BA\cos \theta \]
Where,
$\Phi $ is magnetic flux,
B is magnetic flux,
A is the area and
$\theta $ is the angle between the area of the magnetic field and the perpendicular vector.

Complete answer:
According to the question, it is given that
The diameter of the coil is 21 cm i.e., 0.21 m.
Magnetic field is i.e.,$B = {10^{ - 4}}T$
And the plane of the coil makes an angle of \[\cos {30^ \circ }\].

Now let’s substitute all the given values in the above formula,
\[\Phi = {10^{ - 4}} \times \dfrac{\pi }{4} \times {\left( {0.21} \right)^2} \times \cos {60^ \circ }\]
\[ \Rightarrow \Phi = {10^{ - 4}} \times \dfrac{\pi }{4} \times {\left( {0.21} \right)^2} \times \dfrac{1}{2}\]
\[ \Rightarrow \Phi = 1.73 \times {10^{ - 6}}{\rm{Wb}}\]

Hence option (b) is correct.

Note: A fundamental property of electromagnetism known as Faraday's law of induction describes how a magnetic field will interact with an electric circuit to produce an electromotive force or electromagnetic induction. Note that the SI unit of magnetic flux is Weber.