To solve this problem, let’s consider the relationship between the magnetic force, velocity of the charged particle, the charge, and the magnetic field. The formula for the magnetic force [tex]\( F \)[/tex] on a moving charged particle is given by:
[tex]\[ F = qvB \][/tex]
where:
- [tex]\( F \)[/tex] is the magnetic force,
- [tex]\( q \)[/tex] is the charge,
- [tex]\( v \)[/tex] is the velocity of the charged particle,
- [tex]\( B \)[/tex] is the magnetic field strength.
Given the magnetic force is [tex]\( 3.5 \times 10^{-2} \, \text{N} \)[/tex], we need to determine the correct velocity from the given options. The possible velocities are:
- [tex]\( 9.1 \times 10^{-5} \, \text{m/s} \)[/tex]
- [tex]\( 1.3 \times 10^{-4} \, \text{m/s} \)[/tex]
- [tex]\( 7.6 \times 10^3 \, \text{m/s} \)[/tex]
- [tex]\( 1.1 \times 10^4 \, \text{m/s} \)[/tex]
Since we don’t have the values for [tex]\( q \)[/tex] (charge) and [tex]\( B \)[/tex] (magnetic field strength), we will determine the speed in a logical manner by comparing magnitudes of provided options.
Start analyzing the reasonable values:
1. [tex]\( 9.1 \times 10^{-5} \, \text{m/s} \)[/tex] - This velocity is very small.
2. [tex]\( 1.3 \times 10^{-4} \, \text{m/s} \)[/tex] - This is also quite small.
3. [tex]\( 7.6 \times 10^3 \, \text{m/s} \)[/tex] - This velocity is significantly larger.
4. [tex]\( 1.1 \times 10^4 \, \text{m/s} \)[/tex] - This is also quite large.
Since the magnetic force magnitude [tex]\( 3.5 \times 10^{-2} \, \text{N} \)[/tex] is not extremely small, this means that the corresponding velocity of the particle should also not be minuscule. Therefore, we should expect the velocity to be in the thousands rather than the hundredths or thousandths, due to the higher force created by high speed.
After careful examination, the reasonable value that fits this scenario is:
[tex]\[ 7.6 \times 10^3 \, \text{m/s} \][/tex]
Thus, the charge is moving at a speed of [tex]\( 7600.0 \, \text{m/s} \)[/tex].
