In a region, magnetic field along positive x axis changes with time according to the given graph.

A positively charged particle is projected from origin at an angle tetha zero with the positive x-axis in first quadrant of x dash y plane. If the time period, pitch and radius of helical path are T zero, P zero and R zero respectively, then which of the following statement is correct:

As the magnetic field is along the x-axis, the magnetic force will be along (–) z-axis from t = 0 to t = T₀ and along (+)ve z-axis from t = T₀ to t = 2T₀.
For t = 0 to t = T₀ :–

$\text{ At t }=\frac{{\mathrm{T}}_0}{2};\mathrm{x}\text{-coordinate }=\frac{\left({\mathrm{V}}_0\cos \mathrm{\theta }\right){\mathrm{T}}_0}{2}=\frac{{\mathrm{P}}_0}{2}$
$\left(\text{ Since pitch }={\mathrm{P}}_0=\left({\mathrm{V}}_0\cos \mathrm{\theta }\right){\mathrm{T}}_0\right)$
y-coordinate = 0 (from figure)
and z-coordinate = – 2 R₀ (from figure)
Hence (A) is correct.
Similarly at $\mathrm{t}=\frac{3{\mathrm{T}}_0}{2}$;
coordinates are $\left(\frac{3{\mathrm{P}}_0}{2},0,2{\mathrm{R}}_0\right)$ Hence (B) is correct.
Note : z -coordinate will be + 2R₀, because from t = T₀ to t = 2T₀, direction of changes.
As the charge will perform circular motion about x-axis, the two extremes from x-axis are 2R₀ from each other.
Hence (C) is also correct.
Hence only (D) is incorrect.