Magnetic field in a space is given as `B = -(B_(o)x)/(R )hat(k)`. A circular ring of radius R having current I lies in the space with centre at origin as shown in the figure. Find the magnitude of net magnetic force acting on the circular ring due to the magnetic field.

Options

A. `2iB_(0)R`
B. `pi iB_(0)R`
C. `2pi i B_(0)R`
D. xero

Answer

B

Explanation

`F_("net") = int "force on idy"`
`= 4("idy") ((B_(0))/(R )) (x)`
`= 4i(B_(0))/(R ) underset(0)overset(R )int sqrt R^(2) - y^(2) dy`
`= piiB_(0)R`