Calculate the magnetic force on a proton given its charge, velocity, and the magnetic field.

Here are the solutions to the questions:

4.6. Magnetic Force on a Proton

• Given:

  • Charge of proton, $q = +1.602 \times 10^{-19}\,\text{C}$
  • Velocity, $\vec{v} = (2\hat{i} - 4\hat{j} + \hat{k})\,\text{m/s}$
  • Magnetic field, $\vec{B} = (\hat{i} + 2\hat{j} - \hat{k})\,\text{T}$

• Step 1: Calculate the cross product $\vec{v} \times \vec{B}$.

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