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A Line Charge λ per Unit Length is Lodged Uniformly onto the Rim of a Wheel of Mass M And Radius R. the Wheel Has Light Non-conducting Spokes and is Free to Rotate Without Friction About Its Axis - Physics

A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Fig. 6.22). A uniform magnetic field extends over a circular region within the rim. It is given by,

= − B0 (≤ aR)

= 0 (otherwise)

What is the angular velocity of the wheel after the field is suddenly switched off?

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Solution

Line charge per unit length 

Where,

= Distance of the point within the wheel

Mass of the wheel = M

Radius of the wheel = R

Magnetic field, `vecB=-B_0hatk`

At distance r,themagnetic force is balanced by the centripetal force i.e.,

`BQv=(mv^2)/r`

Where 

v=linear velocity of the wheel

`therefore B2pirlambda=(Mv)/r`

`v=(B2pilambdar^2)/M`

∴Angular velocity, `omega=v/r=(B2pilambdar^2)/(MR)`

For r `<= ` and a <R, we get :

`omega=-(2piBa^2lambda)/(MR)hatk`

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 6 Electromagnetic Induction
Q 17 | Page 232
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