A light charged particle is revolving in a circle of radius 'r' in electrostatic attraction of a static heavy particle with opposite charge. How does the magnetic field 'B' at the centre of the circle due to the moving charge depend on 'r' ?

Options

A. `B prop (1)/( r )`
B. `B prop (1)/(r^(2))`
C. `B prop (1)/(r^(3//2))`
D. `B prop (1)/(r^(5//2))`

Answer

D

Explanation

Electrostatic force of attraction `F_(e )= (KqQ)/(r^(2))`
For circular motion of the charged particle, `F_(c )= F_(e )`
`(mv^(2))/(r )= (KqQ)/(r^(2)) rArr v prop (1)/(sqrtr)`
Time period, `T= (2pi r)/(v) rArr T prop (1)/(sqrtr)`
Time period, `T= (2pi r)/(v) rArr T prop (r )/(v)`
`T prop r^(3//2)`
Current flow, `I prop (Q)/(T) :. I prop r^(-3//2)`
Now, magnetic field, `B= (mu_(0)I)/(2r)`
`rArr B prop (I)/(r ):. B prop r^(-5//2)` (using (i))