To determine the strength of the magnetic field, we use the formula for the magnetic force experienced by a charged particle moving perpendicular to the magnetic field:
[tex]\[ F = q \cdot v \cdot B \][/tex]
Where:
- [tex]\( F \)[/tex] is the magnetic force,
- [tex]\( q \)[/tex] is the charge of the particle,
- [tex]\( v \)[/tex] is the velocity of the particle,
- [tex]\( B \)[/tex] is the magnetic field strength (which we need to find).
Given values:
- Force ([tex]\( F \)[/tex]) = [tex]\( 2.2 \times 10^{-15} \)[/tex] newtons,
- Charge ([tex]\( q \)[/tex]) = [tex]\( -1.6 \times 10^{-19} \)[/tex] coulombs,
- Velocity ([tex]\( v \)[/tex]) = [tex]\( 3.7 \times 10^4 \)[/tex] meters/second.
First, rearrange the formula to solve for [tex]\( B \)[/tex]:
[tex]\[ B = \frac{F}{q \cdot v} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ B = \frac{2.2 \times 10^{-15}}{-1.6 \times 10^{-19} \cdot 3.7 \times 10^4} \][/tex]
Perform the calculation inside the denominator first:
[tex]\[ q \cdot v = -1.6 \times 10^{-19} \cdot 3.7 \times 10^4 = -5.92 \times 10^{-15} \][/tex]
Next, divide the force by this result:
[tex]\[ B = \frac{2.2 \times 10^{-15}}{-5.92 \times 10^{-15}} = -0.3716216216216216 \][/tex]
Since the question asks for the magnitude of the magnetic field, we take the absolute value:
[tex]\[ |B| = 0.3716216216216216 \][/tex]
So, the strength of the magnetic field is approximately [tex]\( 0.37 \)[/tex] teslas. Therefore, the correct answer is:
C. 0.37 teslas
