Questions: Determine the magnetic field strength acting on a positron travelling at 7.31 x 10^7 m / s that experiences a magnetic force of 5.38 x 10^-13 N.

Solution Steps

We need to determine the magnetic field strength \( B \) acting on a positron. We are given:

• The velocity of the positron \( v = 7.31 \times 10^{7} \, \text{m/s} \).
• The magnetic force \( F = 5.38 \times 10^{-13} \, \text{N} \).

The magnetic force \( F \) on a charged particle moving in a magnetic field is given by the equation: \[ F = qvB \sin \theta \] where:

• \( q \) is the charge of the particle,
• \( v \) is the velocity of the particle,
• \( B \) is the magnetic field strength,
• \( \theta \) is the angle between the velocity and the magnetic field.

For maximum force, \(\theta = 90^\circ\) and \(\sin \theta = 1\).

Since the positron is a particle with the same charge magnitude as an electron, \( q = 1.602 \times 10^{-19} \, \text{C} \).

Rearrange the formula to solve for \( B \): \[ B = \frac{F}{qv} \]

Substitute the given values: \[ B = \frac{5.38 \times 10^{-13} \, \text{N}}{(1.602 \times 10^{-19} \, \text{C})(7.31 \times 10^{7} \, \text{m/s})} \]

Perform the calculation: \[ B = \frac{5.38 \times 10^{-13}}{1.602 \times 10^{-19} \times 7.31 \times 10^{7}} \]

\[ B = \frac{5.38 \times 10^{-13}}{1.171 \times 10^{-11}} \]

\[ B \approx 0.0459 \, \text{T} \]

Final Answer