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 an axis passing through its centre and perpendicular to its plane, as shown in the figure. At what value of x , the disc will lift off from the surface.

Question

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 an axis passing through its centre and perpendicular to its plane, as shown in the figure. At what value of x , the disc will lift off from the surface.,

MARKS App · Accepted Answer

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

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