Force on a Current-Carrying Conductor in a Magnetic Field

Introduction

A current-carrying conductor experiences a force when placed in an external magnetic field. This phenomenon is the basis for electric motors and other electromagnetic devices. The magnitude and direction of this force depend on the current, the length of the conductor, the magnetic field strength, and the angle between the conductor and the magnetic field.

KEY TAKEAWAY: A current-carrying wire in a magnetic field experiences a force. This force is the foundation of electric motors.

Key Equation: F = nIlB

The force on a current-carrying conductor in a magnetic field is given by the equation:

$$F = nIlB\sin\theta$$

Where:

• $F$ = Force on the conductor (N)
• $n$ = Number of loops/turns in the conductor
• $I$ = Current in the conductor (A)
• $l$ = Length of the conductor within the magnetic field (m)
• $B$ = Magnetic field strength (T)
• $\theta$ = Angle between the direction of the current and the magnetic field

In VCE Physics, we primarily consider two scenarios:
1. Perpendicular: The conductor is perpendicular to the magnetic field ($\theta = 90^\circ$, $\sin\theta = 1$), so the equation simplifies to $F = nIlB$.
2. Parallel: The conductor is parallel to the magnetic field ($\theta = 0^\circ$, $\sin\theta = 0$), so the force is zero ($F = 0$).

VCAA FOCUS: VCAA exams often focus on scenarios where the current and magnetic field are either perpendicular or parallel. Make sure you understand when to apply $F = nIlB$ and when $F=0$.

Determining the Direction of the Force

The direction of the force on the conductor can be determined using the right-hand palm rule.

1. Point your fingers in the direction of the magnetic field ($B$).
2. Point your thumb in the direction of the conventional current ($I$).
3. Your palm faces the direction of the force ($F$).

REMEMBER: Use the RIGHT hand for the force on a conductor, not the left!

Factors Affecting the Force

The magnitude of the force on a current-carrying conductor in a magnetic field is affected by the following factors:

STUDY HINT: Practice applying the right-hand palm rule with various configurations of current and magnetic field direction to become proficient.

Practical Investigation

Aim

To investigate the relationship between the force on a current-carrying conductor in a magnetic field and the current flowing through the conductor.

Method

1. Set up a circuit with a power supply, ammeter, variable resistor, and a straight conductor placed between the poles of a strong magnet.
2. Use a balance to measure the force on the magnet (which is equal and opposite to the force on the conductor).
3. Vary the current using the variable resistor and record the corresponding force.
4. Ensure the conductor is perpendicular to the magnetic field.

Variables

• Independent Variable: Current ($I$)
• Dependent Variable: Force ($F$)
• Controlled Variables: Magnetic field strength ($B$), Length of conductor ($l$)

Analysis

Plot a graph of force ($F$) vs. current ($I$). The graph should be a straight line passing through the origin, indicating a direct proportional relationship: $F \propto I$. The gradient of the graph is equal to $n l B$.

Precautions

• Use a strong magnet to produce a measurable force.
• Ensure the conductor is perpendicular to the magnetic field.
• Use an accurate ammeter and balance.
• Consider the effect of the Earth’s magnetic field.

EXAM TIP: Be prepared to describe a practical investigation to verify $F = nIlB$, including identifying variables, controls, and potential sources of error.

Examples

Example 1

A straight conductor of length 0.2 m carries a current of 5 A perpendicular to a magnetic field of 0.8 T. Calculate the force on the conductor.

Solution:
$F = nIlB = 1 \times 5 \times 0.2 \times 0.8 = 0.8 \, \text{N}$

Example 2

A coil of 100 turns, each with a length of 0.15 m, carries a current of 2 A in a magnetic field of 0.5 T. The coil is perpendicular to the field. Calculate the force on the coil.

Solution:
$F = nIlB = 100 \times 2 \times 0.15 \times 0.5 = 15 \, \text{N}$

COMMON MISTAKE: Forgetting to include the number of turns ($n$) in the calculation when dealing with a coil.

Relationship to Electric Motors

The force on a current-carrying conductor in a magnetic field is the principle behind the operation of electric motors. A current-carrying loop placed in a magnetic field experiences a torque due to the forces on different segments of the loop. This torque causes the loop to rotate, converting electrical energy into mechanical energy.

APPLICATION: Electric motors use the force on current-carrying conductors in magnetic fields to convert electrical energy into rotational mechanical energy.