Answer

Verified

19.8k+ views

**Hint:**According to Faraday’s law of electromagnetic induction “When the flux of magnetic field through the area bounded by two consecutive spokes changes, an emf between the axle and the rim of the wheel will produce”.

The emf is given by

\[\varepsilon = - \dfrac{{d\phi }}{{dt}}\]

Where, \[\phi = \int {\vec B.d\vec s} \] is the flux of the magnetic field through the area.

**Complete step by step answer:**

Given

Number of spokes = 10

Length of each spoke or radius of the wheel (r) = 0.5 m

Angular speed of the wheel = 120 rev/min = \[4\pi {\text{ rad/s}}\]

Earth’s magnetic field (\[{B_h}\]) = 0.4 G =\[0.4 \times {10^4}T\]

Consider the (A) area covered by an angle is θ.

So, \[A = \pi {r^2}\dfrac{\theta }{{2\pi }}\]

\[\therefore A = {r^2}\dfrac{\theta }{2}\]

Now, The induced emf \[\varepsilon = - \dfrac{{d\phi }}{{dt}} = - \dfrac{{d(BA)}}{{dt}}\]

\[ \Rightarrow \varepsilon = - \dfrac{{Bd(A)}}{{dt}}\]……………….. (ii)

Substitute the given values in the equation (ii), we get

\[\Rightarrow \varepsilon = \dfrac{{2\pi \times 2 \times 0.4 \times {{10}^{ - 4}} \times {{(0.5)}^2}}}{2} = 6.28 \times {10^{ - 5}}V\]

\[\therefore \varepsilon = 0.628mV\]

**Hence, Option (B) is the correct answer.**

**Note:**Magnetic flux changes by change in:-

(i) Magnitude of magnetic field

(ii) Crossing Area and

(iii) Angle between magnetic field vector and area vector.

The direction of the induced magnetic field in a loop can be obtained by using an electromagnetic induction equation. If the flux increases with time, \[\dfrac{{d\phi }}{{dt}}\]is positive and ε will be negative similarly when \[\dfrac{{d\phi }}{{dt}}\]is negative ε will be positive.

Recently Updated Pages

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

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

IfFxdfrac1x2intlimits4xleft 4t22Ft rightdt then F4-class-12-maths-JEE_Main

Three point particles of mass 1 kg 15 kg and 25 kg class 11 physics JEE_Main

A rod of certain length is acted by two equal forces class 11 physics JEE_Main

Other Pages

In order to convert Aniline into chlorobenzene the class 12 chemistry JEE_Main

Give one chemical test to distinguish between the following class 12 chemistry JEE_Main

Assertion The melting point Mn is more than that of class 11 chemistry JEE_Main

Chlorobenzene is extremely less reactive towards a class 12 chemistry JEE_Main

The correct order increasing acidic strength is A Phenol class 12 chemistry JEE_MAIN

Electric field due to uniformly charged sphere class 12 physics JEE_Main