A charged particle of mass 5 mg and charge `q= +2 mu C` has velocity `vec v = 2 hat i - 3 hat j + 4 hat k.` Find out the magnetic force on the charged particle and its acceleration at this instant due to magnetic field `vec B = 3 hat j - 2 hat k. vec v and vec B` are in `ms^-1 and Wbm^-2` , respectively.

Explanation

To find the magnetic force on a charged particle and its acceleration, we can follow these steps:

### Step 1: Identify the given values
- Mass of the particle, \( m = 5 \, \text{mg} = 5 \times 10^{-6} \, \text{kg} \)
- Charge of the particle, \( q = +2 \, \mu \text{C} = 2 \times 10^{-6} \, \text{C} \)
- Velocity of the particle, \( \vec{v} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k} \, \text{m/s} \)
- Magnetic field, \( \vec{B} = 3 \hat{j} - 2 \hat{k} \, \text{Wb/m}^2 \)

...