nice 1 for all ...................

a charge q wit mass m moves in a non uniform mag field in a plane perp. to the field .....B=B0/x.......mag field is along y axis ......

particle strats frm x=a wit v0 dir. along x axis ...... how far will particle travel bfr its velocity becomes || to z axis

4 Answers

Since there is no velocity in the Y-direction,
u=u_x+u_z and B=B₀/x

equation of motion along x and z axis is
dv_x/dt=-qB₀v_z/mx

dv_z/dt=-qB₀v_x/mx

adding 1 and 2,
v_x²+v_z²=constant=v₀²

v_z=âˆšv₀²-v_x²

substituting in equation 1, and re-writing,
v_xdv_x/dx=-qB₀âˆšv₀²-v_x²/mx

Integrating we get,
âˆšv₀²-v_x²=qB₀lnx+C

initial conditions are x=a, v=v₀
Therefore,
C=qB₀lnx/a
when velocity becums || to z-axis, v_x=0
x_max=ae^mv₀/qB₀

Hey injun, how did you get the expression for integration??

even my ans cumes out to b....
x=ae^mv₀/bq

post the ans...

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