A charged particle of charge e and mass m is moving in an electric field `vecE` and magnetic field `vecB`. Construct dimensionless quantities and quantities of dimention `[T]^-1`.

Explanation

To solve the problem of constructing dimensionless quantities and quantities with dimension \([T]^{-1}\) from the given parameters (charge \(e\), mass \(m\), electric field \(\vec{E}\), and magnetic field \(\vec{B}\)), we will follow these steps:

### Step 1: Identify the Dimensions of Given Quantities
1. **Charge \(e\)**: The dimension of charge is represented as \([Q] = [A][T]\).
2. **Mass \(m\)**: The dimension of mass is \([M]\).
3. **Electric Field \(\vec{E}\)**: The electric field can be derived from the force equation \(F = qE\). The dimension of force is \([F] = [M][L][T]^{-2}\). Thus,
\[
[E] = \frac{[F]}{[Q]} = \frac{[M][L][T]^{-2}}{[A][T]} = [M][L][A]^{-1}[T]^{-3}
...