Question

A positive charge q is distributed over a circular ring of radius a. It is placed in a horizontal plane and is rotated about its axis at a uniform angular speed ω. A horizontal magnetic field B exists in the space. The torque acting on the ring due to the magnetic force is ______.

Options

• `1/2 "q" omega "a"^2 "B"`

• `1/2 "q" omega "a B"`

• `1/2 "q" omega^2 "a B"`

• `"q" omega "a"^2 "B"`

Answer 1

A positive charge q is distributed over a circular ring of radius a. It is placed in a horizontal plane and is rotated about its axis at a uniform angular speed ω. A horizontal magnetic field B exists in the space. The torque acting on the ring due to the magnetic force is `underline(1/2 "q" omega "a"^2 "B")`.

Explanation:

Using torque T = `"M" xx "B" = "IA" xx "B" = "q"/"t" xx pi"a"^2 xx "B"`

`= "qw"/(2pi) xx pi"a"^2 xx "B"     ...[because omega = (2pi)/"t"  "or", "t" = (2pi)/omega]`

`therefore "T" = 1/2 "q" omega "a"^2 "B"`