NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice
A thin non conducting disc of mass M = 2 kg , charge Q = 2 × 10 - 2 C and radius R = 1 6 m is placed on a frictionless horizontal plane with its centre at the origin of the coordinate system. A non-uniform, radial magnetic field B → = B 0 r ^ exists in space, where B 0 = 10 T and r ^ is a unit vector in the radially outward direction. The disc is set in motion with an angular velocity ω = x × 10 2 rad s - 1 , about a
Correct answer
9
Step-by-step solution
The force an any small part of the disc is in the vertically upward direction d F = Q π R 2 2 π r   d r ω r   B 0 d F = 2 Q ω B 0 R 2   r 2   d r F = 2 3 Q ω B 0 R = M g   ⇒ ω = 3 M g 2 Q B 0 R = 3 × 2 × 10 2 × 2 × 10 - 2 × 10 × 1 6 = 9 × 10 2   r a d   s - 1