# 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?

#### 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?

#### APPEARS IN

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