Question

1. an electron experiences a downward magnetic force of 7.20×10⁻¹⁴ n when it is travelling at 3.00×10⁵ m/s south through a magnetic field. calculate the magnitude of the magnetic field and determine its direction using the left - hand rule. (3 marks). explain all finger directions and the palm direction (1 mark)

Explanation:

Step1: Recall the magnetic force formula

The formula for the magnetic force on a charged particle is \( F = qvB\sin\theta \). For an electron moving perpendicular to the magnetic field (\(\theta = 90^\circ\), so \(\sin\theta=1\)), the formula simplifies to \( F = |q|vB \) (we use the magnitude of the electron's charge \( |q| = 1.6\times 10^{-19}\, \text{C} \)). We need to solve for \( B \), so rearranging the formula gives \( B=\frac{F}{|q|v} \).

Step2: Substitute the given values

We know \( F = 7.20\times 10^{-14}\, \text{N} \), \( |q| = 1.6\times 10^{-19}\, \text{C} \), and \( v = 3.00\times 10^{5}\, \text{m/s} \). Substituting these into the formula for \( B \):

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Step3: Determine the direction using the left - hand rule (for negative charges, we can use the left - hand rule by considering the direction of the current opposite to the electron's velocity)

• The electron is moving south, so the direction of the current (conventional current) is north (since current is opposite to electron's velocity).
• The force on the electron is downward. For a negative charge, we use the left - hand rule:
• Point your left hand fingers in the direction of the magnetic field (we will find this).
• Point your middle finger in the direction of the current (north).
• The thumb points in the direction of the force on a positive charge, but for a negative charge, the force is opposite. Since the force on the electron is downward, the thumb (for positive charge force) would be upward, but we reverse it for the electron.
• Using the left - hand rule: middle finger (current) north, thumb (force on positive charge) upward (so force on electron is downward), then the index finger (magnetic field) points west.

• Finger directions: Middle finger (current) - north, Index finger (magnetic field) - west, Thumb (force on positive charge) - upward (force on electron is downward, opposite to thumb direction). Palm direction: The palm faces in the direction of the force on a positive charge (upward), but the electron experiences a force downward (opposite to palm direction for positive charge, consistent with electron being negative).

Answer:

The magnitude of the magnetic field is \( \boldsymbol{1.5\, \text{T}} \). The direction of the magnetic field is west.