Answer :
To find the charge, we can use the formula for the magnetic force acting on a moving charge:
[tex]\[ F = q \cdot v \cdot B \cdot \sin(\theta) \][/tex]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge,
- \( v \) is the velocity of the charge,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity and the magnetic field.
Given the problem:
- \( F = 2.89 \times 10^{-7} \) N
- \( v = 288 \) m/s
- \( B = 2.77 \times 10^{-5} \) T
- \( \theta = 90^{\circ} \)
Since the angle \(\theta\) is \(90^{\circ}\), \(\sin(90^{\circ}) = 1\). Thus, the formula simplifies to:
[tex]\[ F = q \cdot v \cdot B \][/tex]
Rearrange the formula to solve for \( q \):
[tex]\[ q = \frac{F}{v \cdot B} \][/tex]
Substitute the given values into the formula:
[tex]\[ q = \frac{2.89 \times 10^{-7} \, \text{N}}{288 \, \text{m/s} \times 2.77 \times 10^{-5} \, \text{T}} \][/tex]
[tex]\[ q = \frac{2.89 \times 10^{-7}}{7.9776 \times 10^{-3}} \][/tex]
[tex]\[ q \approx 3.6226434015242685 \times 10^{-5} \, \text{C} \][/tex]
Thus, the charge \( q \) is approximately:
[tex]\[ 3.62 \times 10^{-5} \, \text{C} \][/tex]
So, the charge that experiences the given force under the specified conditions is:
[tex]\[ 3.62 \times 10^{-5} \, \text{C} \][/tex]
[tex]\[ F = q \cdot v \cdot B \cdot \sin(\theta) \][/tex]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge,
- \( v \) is the velocity of the charge,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity and the magnetic field.
Given the problem:
- \( F = 2.89 \times 10^{-7} \) N
- \( v = 288 \) m/s
- \( B = 2.77 \times 10^{-5} \) T
- \( \theta = 90^{\circ} \)
Since the angle \(\theta\) is \(90^{\circ}\), \(\sin(90^{\circ}) = 1\). Thus, the formula simplifies to:
[tex]\[ F = q \cdot v \cdot B \][/tex]
Rearrange the formula to solve for \( q \):
[tex]\[ q = \frac{F}{v \cdot B} \][/tex]
Substitute the given values into the formula:
[tex]\[ q = \frac{2.89 \times 10^{-7} \, \text{N}}{288 \, \text{m/s} \times 2.77 \times 10^{-5} \, \text{T}} \][/tex]
[tex]\[ q = \frac{2.89 \times 10^{-7}}{7.9776 \times 10^{-3}} \][/tex]
[tex]\[ q \approx 3.6226434015242685 \times 10^{-5} \, \text{C} \][/tex]
Thus, the charge \( q \) is approximately:
[tex]\[ 3.62 \times 10^{-5} \, \text{C} \][/tex]
So, the charge that experiences the given force under the specified conditions is:
[tex]\[ 3.62 \times 10^{-5} \, \text{C} \][/tex]
