To determine the magnitude of the magnetic force acting on the charge, we use the formula for the magnetic force on a moving charge:
[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 charge,
- [tex]\( B \)[/tex] is the magnetic field strength.
We are given the following values:
- Charge ([tex]\( q \)[/tex]) = [tex]\( 5.0 \times 10^{-7} \)[/tex] C (Coulombs)
- Velocity ([tex]\( v \)[/tex]) = [tex]\( 2.6 \times 10^5 \)[/tex] m/s (meters per second)
- Magnetic field strength ([tex]\( B \)[/tex]) = [tex]\( 1.8 \times 10^{-2} \)[/tex] T (Tesla)
Substituting these values into the formula, we get:
[tex]\[ F = (5.0 \times 10^{-7} \, \text{C}) \times (2.6 \times 10^5 \, \text{m/s}) \times (1.8 \times 10^{-2} \, \text{T}) \][/tex]
Calculating the product step-by-step:
1. First, multiply the charge and the velocity:
[tex]\[ (5.0 \times 10^{-7}) \times (2.6 \times 10^5) = 1.3 \times 10^{-1} \][/tex]
2. Next, multiply the result by the magnetic field strength:
[tex]\[ (1.3 \times 10^{-1}) \times (1.8 \times 10^{-2}) \][/tex]
3. Finally:
[tex]\[ 1.3 \times 1.8 \times 10^{-1} \times 10^{-2} = 2.34 \times 10^{-3} \, \text{N} \][/tex]
Therefore, the magnitude of the magnetic force acting on the charge is [tex]\(2.34 \times 10^{-3} \, \text{N}\)[/tex].
Comparing this to the provided choices:
- [tex]\(0 \, \text{N}\)[/tex]
- [tex]\(2.3 \times 10^{-3} \, \text{N}\)[/tex]
- [tex]\(23 \, \text{N}\)[/tex]
- [tex]\(2.3 \times 10^{11} \, \text{N}\)[/tex]
The closest and correct choice is:
[tex]\[ 2.3 \times 10^{-3} \, \text{N} \][/tex]
