Two parallel wires in the plane of the paper are distance `X_(0)` apart. A point charge is moving with speed `u` between the wires in the same plane at a distance `X_(1)` from one of the wires. When the wires carry current of magnitude `I` in the same direction , the radfius of curvature of the path of the point charge is `R_(1)`. In contrast, if the currentsd `I` in the two wires have directions opposite to each other, the radius of curvature of the path is `R_(2)`. if `(X_(0))/(X_(1)) = 3`, the value of `( R _(1))/( R_(2))` is

Answer

3

Explanation

`B_(2)=(mu_(0)I)/(2pix_(1))+(mu_(0)I)/(2pi(x_(0)-x_(1)))` (when currents are in opposite direction)
`B_(1)=(mu_(0)I)/(2pix_(1))- (mu_(0)I)/(2pi(x_(0)-x_(1)))`
(2hen currents are in same direction) substiting `x_(1)=(x_(0))/3` (as `(x_(0))/(x_(1))=3)`

`B_(1)=(3mu_(0)I)/(2pix_(0)) - (3mu_(0)I)/(4pix_(0))- (3mu_(0)I)/(4pix_(0))R_(1)=(mv)/(qB_(1))` and `B_(2)=(9mu_(0)I)/(4pix_(0))R_(2)=(mv)/(qB_(2))implies(R_(1))/(R_(2))=(B_(2))/(B_(1))=9/3=3`