To determine the magnitude of the magnetic force acting on a point charge moving in a magnetic field, we use the formula:
[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.
Given:
- The charge, [tex]\( q \)[/tex], is [tex]\( 5.7 \, \mu C \)[/tex] (microcoulombs), which is equivalent to [tex]\( 5.7 \times 10^{-6} \, C \)[/tex].
- The velocity, [tex]\( v \)[/tex], is [tex]\( 4.5 \times 10^5 \, m/s \)[/tex].
- The magnetic field strength, [tex]\( B \)[/tex], is [tex]\( 3.2 \, mT \)[/tex] (milliTesla), which is equivalent to [tex]\( 3.2 \times 10^{-3} \, T \)[/tex].
Let's plug the given values into the formula:
[tex]\[ F = (5.7 \times 10^{-6} \, C) \times (4.5 \times 10^5 \, m/s) \times (3.2 \times 10^{-3} \, T) \][/tex]
Perform the multiplication step-by-step:
1. Multiply the charge by the velocity:
[tex]\[ 5.7 \times 10^{-6} \, C \times 4.5 \times 10^5 \, m/s = 2.565 \times 10^{-1} \][/tex]
2. Multiply the result by the magnetic field strength:
[tex]\[ 2.565 \times 10^{-1} \times 3.2 \times 10^{-3} \, T = 8.208 \times 10^{-3} \, N \][/tex]
Therefore, the magnitude of the magnetic force acting on the charge is [tex]\( 0.008208 \, N \)[/tex], which is equivalent to:
[tex]\[ 8.208 \times 10^{-3} \, N \][/tex]
Now, comparing this result with the provided options:
- [tex]\( 6.6 \times 10^{-3} N \)[/tex]
- [tex]\( 4.9 \times 10^{-3} N \)[/tex]
- [tex]\( 4.9 \times 10^3 N \)[/tex]
- [tex]\( 6.6 \times 10^3 N \)[/tex]
None of the provided options are correct based on the detailed calculation. The correct answer should be [tex]\( 8.208 \times 10^{-3} \, N \)[/tex] which is not listed.
