28.6
Magnetic Force
In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created…
Consider two wires connected to a battery.
If the currents' directions are opposite, the wires repel. If the directions are the same, the wires attract.
When a test charge is placed nearby, it experiences no force, since the wires are electrically neutral. So, the force acting between the wires is not electric; this is known as the magnetic force.
If a magnetic compass is placed near the wire, the needle experiences a force and is aligned tangentially to a circle around it. As a result, concentric loops of magnetic fields are formed around the wire.
If the thumb points in the current's direction, the wrapped fingers provide the direction of the magnetic field.
For a wire with a current in the upward direction, the magnetic field points inward into the plane, and the magnetic force points to the left.
This combination of directions satisfies the right-hand rule. The magnetic force on a test charge Q moving with velocity v in a magnetic field B is Q multiplied by the cross-product of v and B, called the Lorentz force.
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Q1: Why do two current-carrying wires attract or repel each other?
Two current-carrying wires experience magnetic force based on current direction. When currents flow in the same direction, the wires attract; when opposite, they repel. This force is not electric because the wires are electrically neutral. The interaction arises from the magnetic fields created by moving charges in each wire.
Q2: What is the Lorentz force and how is it calculated?
The Lorentz force is the magnetic force on a moving charge Q in a magnetic field B. It equals Q multiplied by the cross-product of velocity v and magnetic field B. This force depends on charge magnitude, field strength, and velocity direction. The right-hand rule determines the force direction relative to velocity and field.
Q3: How does the right-hand rule predict magnetic field direction around a current-carrying wire?
Point your thumb in the current's direction; your wrapped fingers show the magnetic field direction. For upward current, the field points inward into the plane. Concentric loops of magnetic field form around the wire. This rule combines current direction with resulting field orientation to predict magnetic force direction.
Q4: Why does magnetic force not do work on a moving charged particle?
Magnetic force is always perpendicular to both velocity and the magnetic field. Since work requires force component parallel to displacement, perpendicular force does zero work. The magnetic force can only change a particle's direction of motion, not its speed. Particle kinetic energy remains constant under magnetic force alone.
Q5: What are the four main properties of magnetic force on a moving charge?
First, force magnitude is proportional to charge magnitude. Second, it is proportional to magnetic field strength. Third, magnetic force depends on velocity; stationary charges experience no magnetic force. Fourth, the force is always perpendicular to both velocity and field, distinguishing it from constant electric force.
Q6: How does a magnetic compass needle respond to a current-carrying wire?
A compass needle aligns tangentially to concentric circles of magnetic field surrounding the wire. The needle experiences magnetic force from the field created by moving charges in the wire. This demonstrates that magnetic fields are real physical entities that exert forces on magnetic materials and moving charges.
Q7: Why is magnetic force absent on a stationary charged particle?
Magnetic force depends on charge velocity; a stationary charge has zero velocity. The Lorentz force equation F = Q(v × B) yields zero when v equals zero. Only moving charges experience magnetic force. This distinguishes magnetic forces from electric forces, which act on charges regardless of motion.