Answer

Verified

53.7k+ views

**Hint:**We can solve this question using the equation for calculating flux. Flux is the dot product of the magnetic field and the area. It is given as

$\phi = BA\cos \theta $

Where B is the magnetic field , A is the area and the angle $\theta $ is the angle between the area vector and the magnetic field.

By substituting the given values in this equation we can find the value of the magnetic field.

**Complete step by step solution:**

It is given that a flux of $1\,mWb$ passes through a strip.

Flux is a measure of the number of magnetic field lines passing through a given area. It is denoted as $\phi $

It is given by the formula

$ \Rightarrow \phi = BA\cos \theta $

Where B is the magnetic field and A is the area of the cross section.

Here, $\theta $ is the angle made by the direction of the magnetic field with the area vector. Area vector is the perpendicular vector drawn at the surface of area.

Since flux is given, we can write

$\phi = 1\,mWb = 1 \times {10^{ - 3}}Wb$

Area of the strip is given as $0.02{m^2}$

$ \Rightarrow A = 0.02{m^2}$

The direction of the uniform field makes an angle ${60^ \circ }$ with the strip. Thus, the angle between area vector and magnetic field will be ${90^ \circ } - {60^ \circ } = {30^ \circ }$

We need to find the value of magnetic field B .

For this let us use the equation for calculating flux.

$\phi = BA\cos \theta $

On substituting the given values we get

$1 \times {10^{ - 3}} = B \times 0.02 \times \cos \,{30^0}$

$ \Rightarrow B = \dfrac{{{{10}^{ - 3}}}}{{2 \times {{10}^{ - 2}} \times \dfrac{{\sqrt 3 }}{2}}}$

$\therefore B = 0.058\,T$.

This is the value of the magnetic field.

**So, the correct answer is option B.**

**Note:**Remember that the angle $\theta $ in the equation for calculating flux is the angle between area vector and the magnetic field. An area vector is a normal vector drawn at the surface of a plane. The given angle ${60^ \circ }$ is the angle made by the plane with the field. So subtract this angle from ${90^ \circ }$ to get the angle made by the area vector with the magnetic field.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

A given ray of light suffers minimum deviation in an class 12 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

Oxidation of succinate ion produces ethylene and carbon class 12 chemistry JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main