A charged particle moves at 2 point 5 times 10 to the 4th power m/s at an angle of 25 degrees to a magnetic field that has a field strength of 8 point 1 times 10 to the negative 2 power T If the magnetic force is 7 point 5 times 10 to the negative 2 power N , what is the magnitude of the charge?
Answer
A
1 point 0 times 10 to the negative 4 power cap c
B
4 point 1 times 10 to the negative 5 power cap c
C
3 point 7 times 10 to the negative 5 power cap c
D
8 point 8 times 10 to the negative 5 power cap c
Explanation
The magnetic force is F = |q|vB sin θ, so |q| = F/(vB sin θ). Substituting gives |q| = (7.5 × 10⁻²)/[(2.5 × 10⁴)(8.1 × 10⁻²)sin 25°] ≈ 8.8 × 10⁻⁵ C. Therefore, the charge magnitude is 8.8 × 10⁻⁵ C, choice A.
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