In a region, magnetic field along x-axis changes according to the graph given in fig.

If time period, pitch and radius of helix path are `T_0, P_0 and R_0`, respectively, and if the particle is projected at an angle `theta_0` with the positive x-axis towards positive y-axis in x-y plane, then
select the correct statement

Options

A. At `t=(T_0)/2`, coordinates of charge are `((P_0)/2,0,-2R_0)`
B. At `t=(3T_0)/2`, coordinates of charge are `((3P_0)/2,0,2R_0)`
C. At `t=(T_0)/2`, coordinates of charge are `(P_0,0,-2R_0)`
D. At `t=(3T_0)/2`, coordinates of charge are `(3P_0,0,2R_0)`

Answer

(a,b)

Explanation

As The magnetic field is along the x-axis, the magnetic force will be along (-)z-axis at `t=0`. So, the particle will move in helical path along (1). At `t=T_0`, the direction of field chages, so force becomes along +z-direction, and now the particle will move in helical path along(2). It will be moving along x-axis, So that resulting path will be helical.
At `t=(T_0)/2`, particle will be at `E_1`.

x-coordinate=`(P_0)/2` (half of pitch)
y-coordinate=0
and z-coordinate=`-2R_0`
Hence, (a) is correct.
Similarly at `t=(3T_0)/2` particle will be at `E_2`.
`:.` The coordinates are `((3P_0)/2, 0, 2R_0)`
Hence, (b) is correct.
From Fig. we can see that distance between two extrems:
`E_1 and E_2 is 4R_0`.