A particle with charge `7.00 mu C` is moving with velocity `vec v =- (4xx10^3 ms^-1) hat j.` The magnetic force on the particle is measured to be `vec F = +(8.4 xx 10^-2 N) hat i - (5.60 xx 10^-2 N) hat k.`
a. Calculate all the components of the magnetic field you can from this information.
b. Are there components of the magnetic field that cannot be determined by measurement of the force? Explain.
c. Calculate the scalar product `vec B. vec F.` What is the angle between `vec B and vec F`?

Explanation

To solve the problem step by step, let's break it down into parts as specified in the question.

### Part a: Calculate all the components of the magnetic field

1. **Given Information**:
- Charge of the particle, \( q = 7.00 \, \mu C = 7.00 \times 10^{-6} \, C \)
- Velocity of the particle, \( \vec{v} = -4 \times 10^3 \, \hat{j} \, m/s \)
- Magnetic force, \( \vec{F} = 8.4 \times 10^{-2} \, \hat{i} - 5.6 \times 10^{-2} \, \hat{k} \, N \)
...