Force on a current-carrying conductor Revision Notes

When an electric current flows through a conductor placed within a magnetic field, the conductor experiences a force. This force arises because moving charges (electrons) in the conductor interact with the magnetic field.

The force acts perpendicular to both the direction of the current and the magnetic field. This is a vector effect described by Fleming's left-hand rule: if the thumb, first finger, and second finger of the left hand are held mutually perpendicular, the first finger points in the direction of the magnetic field (from north to south), the second finger points in the direction of the current (conventional current, positive to negative), and the thumb points in the direction of the force on the conductor.

The magnitude of the force (F) on a straight conductor of length (L) carrying current (I) in a magnetic field of flux density (B) is given by: F = BIL, where B is in teslas (T), I in amperes (A), L in metres (m), and F in newtons (N). This formula applies when the conductor is perpendicular to the magnetic field lines. If the conductor is at an angle θ to the field, the force is F = BIL sin θ.

To demonstrate the force on a current-carrying conductor in a magnetic field, the following apparatus is required:

A power supply (variable DC source) to provide current.

A straight, rigid conducting wire (e.g., copper wire) mounted so it can move freely or is suspended horizontally between two supports or connected to a sensitive balance or spring scale to detect force direction and magnitude changes (a common setup uses a wire suspended between the poles of a horseshoe magnet). A strong permanent magnet or electromagnet with clearly marked north and south poles to create a uniform magnetic field between the poles. Ammeter to measure current through the wire. Switch to control current flow. Connecting wires and a ruler to measure wire length in the magnetic field region. Clamp stands and holders to secure apparatus safely. Optional: a sensitive force sensor or spring balance to measure force magnitude.

1. Place the straight wire horizontally between the poles of the horseshoe magnet so that the wire lies perpendicular to the magnetic field lines. The magnetic field direction is from the north pole to the south pole of the magnet.

2. Connect the wire in series with the power supply, ammeter, and switch to form a complete circuit.

3. Close the switch to allow current to flow through the wire. Observe the wire carefully for any movement or force indication (e.g., deflection on a spring balance or displacement if suspended). The wire should experience a force perpendicular to both the current and magnetic field directions, causing it to move or exert a measurable force on the support or balance. 4. Reverse the direction of the current by swapping the connections to the power supply or reversing the polarity. Observe that the direction of the force on the wire reverses accordingly, causing movement or force in the opposite direction. 5. Restore the original current direction, then reverse the magnetic field direction by swapping the magnet poles or turning the magnet around. Observe that the force direction on the wire reverses again. 6. Repeat measurements for different current values and record observations to confirm the relationship between current direction, magnetic field direction, and force direction.

• Place wire perpendicular to magnetic field between magnet poles.

Independent variable: direction of current and direction of magnetic field.

Dependent variable: direction and magnitude of force on the conductor (observed as wire movement or force reading).

Control variables: length of wire in magnetic field, strength of magnetic field (magnet type and position), current magnitude (except when testing current direction). Measurements: current (amperes) using ammeter, length of wire in magnetic field (metres) using ruler, force magnitude (newtons) if using a force sensor or spring balance. Repeats: perform multiple trials for each configuration to ensure consistent observations and reduce random errors. Accuracy improvements: use a strong magnet to produce a uniform and strong magnetic field, ensure wire is straight and firmly mounted, use sensitive force measurement devices, and minimise external disturbances such as air currents or vibrations. Safety: ensure power supply voltage and current are within safe limits to avoid overheating the wire or causing electric shock. Switch off power supply when adjusting apparatus.

• Independent variables: current direction, magnetic field direction.

The experiment demonstrates that a current-carrying conductor placed in a magnetic field experiences a force. The direction of this force depends on the directions of both the current and the magnetic field. Reversing the current direction reverses the force direction, as does reversing the magnetic field direction. This confirms the vector nature of the force and the validity of Fleming's left-hand rule.

This principle underlies the operation of electric motors, where forces on current-carrying coils in magnetic fields produce rotational motion.

The magnitude of the force depends on the current, magnetic flux density, and length of the conductor within the field, consistent with the equation F = BIL sin θ (with θ = 90° in this experiment).

When a conductor carrying an electric current is placed in a magnetic field, it experiences a force. This force arises due to the interaction between the magnetic field and the moving charges (electrons) within the conductor.

The force is a vector quantity, meaning it has both magnitude and direction. Understanding the relative directions of the force, magnetic field, and current is essential for analysing electromagnetic devices such as electric motors and loudspeakers.

• Force acts perpendicular to both the magnetic field and the current.
• The magnitude of the force depends on the current, magnetic field strength, length of conductor, and angle between current and field.

The magnetic field (B) is a vector field that exerts forces on moving charges. It is represented by field lines that show the direction a north magnetic pole would move.

Electric current (I) is the flow of electric charge, conventionally taken as the direction positive charges would move.

Both magnetic field and current have specific directions that must be considered when determining the force on the conductor.

• Magnetic field direction is from north to south outside a magnet.
• Current direction is from positive to negative terminal in a circuit.

The right-hand rule is a mnemonic to find the direction of the force on a current-carrying conductor in a magnetic field.

To apply the right-hand rule: point your right-hand thumb in the direction of the current (I), your fingers in the direction of the magnetic field (B), then your palm pushes in the direction of the force (F) acting on the conductor.

This rule applies only when the current and magnetic field are perpendicular; if not, the force is proportional to the sine of the angle between them.

• Thumb = current direction (I)
• Fingers = magnetic field direction (B)
• Palm (or perpendicular direction) = force direction (F)

The magnitude of the force (F) on a conductor of length (L) carrying current (I) in a magnetic field of flux density (B) is given by:

\[ F = BIL \] when the conductor is perpendicular to the magnetic field.

If the conductor is at an angle \( \theta \) to the magnetic field, the force is: \[ F = BIL \sin \theta \] where: B is in teslas (T), I in amperes (A), L in metres (m), and F in newtons (N).

• Force direction is perpendicular to both current and magnetic field.
• Force magnitude depends on the sine of the angle between current and field.

To draw a diagram showing the directions of force, magnetic field, and current:

1. Draw a straight conductor (a line) representing the wire carrying current.

2. Use an arrow along the conductor to indicate the direction of current (I). Conventionally, arrow points from positive to negative terminal in the circuit path, or direction of positive charge flow (opposite to electron flow). 3. Draw magnetic field lines as parallel arrows crossing the conductor at right angles; arrows point from magnetic north to south poles, indicating magnetic field direction (B). 4. Use the right-hand rule to determine the force direction (F): draw an arrow perpendicular to both the current and magnetic field directions, showing the force on the conductor. 5. Label all arrows clearly with I, B, and F respectively.

• Current arrow along conductor line.
• Magnetic field arrows perpendicular to conductor.
• Force arrow perpendicular to both current and magnetic field.

When a charged particle moves through a magnetic field, it experiences a force known as the magnetic component of the Lorentz force. This force acts perpendicular to both the particle's velocity vector and the magnetic field vector.

The magnetic force does not change the speed of the particle but alters its direction, causing the particle to move in a curved path if the magnetic field is uniform and the velocity has a component perpendicular to the field.

The magnitude of the magnetic force F on a charged particle is given by the equation: F = qvB sin θ, where: q is the charge of the particle in coulombs (C), v is the speed of the particle in metres per second (m/s), B is the magnetic flux density in teslas (T), and θ is the angle between the velocity vector and the magnetic field vector.

• Force is zero if the velocity is parallel or antiparallel to the magnetic field (θ = 0° or 180°).

The direction of the magnetic force on a charged particle is found using the right-hand rule (also called Fleming’s left-hand rule for motors, but here specifically the right-hand rule for charged particles):

1. Point your right hand’s fingers in the direction of the particle’s velocity (v).

2. Point your palm or curl your fingers towards the direction of the magnetic field (B). This is the direction the magnetic field lines point (from north to south). 3. Your thumb then points in the direction of the force (F) acting on a positively charged particle.

Because the magnetic force is always perpendicular to the velocity, it acts as a centripetal force causing circular or helical motion of charged particles in magnetic fields.

If the velocity is exactly perpendicular to the magnetic field, the particle moves in a circle of radius r, given by: r = mv / (qB), where m is the particle’s mass in kilograms (kg).

If the velocity has a component parallel to the magnetic field, the particle moves in a helix along the field lines, combining circular motion perpendicular to the field and linear motion parallel to it.

A proton moves horizontally to the right with velocity v in a uniform magnetic field directed vertically upwards. Determine the direction of the magnetic force on the proton.

Step 1: Identify directions: Velocity (v) → right (along x-axis). Magnetic field (B) → upwards (along y-axis).

Step 2: Apply right-hand rule: Point fingers right (velocity), curl fingers up (magnetic field), thumb points out of the page (towards observer). This is the force direction on a positive charge (proton).

To draw a diagram showing the force on a charged particle in a magnetic field:

1. Draw a coordinate system with x, y, and z axes.

2. Represent the velocity vector as an arrow along one axis (e.g., right along x-axis). Label it v. 3. Represent the magnetic field vector as an arrow along a different axis (e.g., upwards along y-axis). Label it B. 4. Use the right-hand rule to determine the force direction and draw the force vector perpendicular to both v and B (e.g., out of the page along z-axis). Label it F.