# Difficult to imagine!

**Electricity and Magnetism**Level 3

A charged particle of mass \(\displaystyle m\) and charge \(\displaystyle q\) is released from the origin with a velocity \(\displaystyle \vec{v} = v_o \hat{i}\) in a uniform magnetic field \(\displaystyle \vec{B} = \frac{B_o}{2}\hat{i} + \frac{\sqrt{3}B_o}{2}\hat{j}\)

If \(\displaystyle R\) represents the **pitch** (in meters) of the helical path described by the particle, the find the value of \((R-11)\) to the nearest **integer**.

**Details and Assumptions:**

\(\bullet\) Consider a standard Right-handed Cartesian coordinate system.

\(\bullet\) \(\displaystyle m = 0.1g\)

\(\bullet\) \(\displaystyle q = 10\mu C\)

\(\bullet\) \(\displaystyle v_o = 20 m/s\)

\(\bullet\) \(\displaystyle B_o = 8 T\)