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)l)/(2pix_(1))+(mu_(0)l)/(2pi(x-x_(1)))`(opposite)
`B_(1)=(mu_(0)l)/(2pix_(1))-(mu_(0)l)/(2pi(x-x_(1)))`(same)
Case-I When current is in the same direction
`B=B_(1)=(3mu_(0)l)/(2pix_(0))-(3mu_(0)l)/(4pix_(0))=(3mu_(0)l)/(4pix_(0))rArrR_(1)=(mv)/(qB_(1))`
Case-2 When current is in opposite direction
`B=B_(2)=(9mu_(0)l)/(4pix_(0)) rArr R_(2)=(mv)/(qB_(2)) rArr R_(1)/R_(2)=B_(2)/B_(1)=9/3=3`