A proton is moving along the negative direction of X-axis in a magnetic field directed along the positive direction of Y-axis. The proton will be deflected along the negative direction of

Explanation

The induced current is in the counter clockwise direction and the magnetic force on the bar is given by `F_(B) = -ilB`. The negative sign indicates that the force is towards the left and retards motion.
`F=ma" "-ilB=m. (dv)/(dt)`
Because the force depends on current and the current depends on the speed, the force is not constant and the acceleration of the bar is not constant. The induced current is given by `i=(Blv)/(R)" "=ilB=m.(dv)/(dt)`
`-((Blv)/(R))lB=m.(dv)/(dt) implies (dv)/(v)= -(B^(2)l^(2))/(mR)dt`
`int_(V_(1))^(V) (dv)/(v)= -(B^(2)l^(2))/(mR)t=(-t)/(T)` where `T= (mR)/(B^(2)l^(2)) implies v=v_(i)e^(-(t)/(T))`
The speed of the bar therefore decreases exponentially with time under the action of magnetic retarding force.
`emf=iR = Blv_(i)e^(-(t)/(T))`
current: `i=(Blv)/(R)=(Bl)/(R)v_(i)e^(-(t)/(T))`