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Magnetic Force on a Current-Carrying Wire

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Magnetic Force on a Current-Carrying Wire

Physics

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Students use a current balance to observe magnetic force on a current-carrying wire.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Explain the relationship between the direction of current in a wire and the magnetic force it feels.
  • Explain the relationship between the direction of an external magnetic field and the magnetic force felt by a current-carrying wire.
  • Understand the relationship between the length of a wire in an external magnetic field and the magnetic force felt by a current-carrying wire.
  • Understand how the angle between the direction of the external magnetic field and the current-carrying wire affects and the magnetic force felt by a current-carrying wire.
  • Calculate the magnetic force acting on a current-carrying wire.

Everything You'll Have Covered

Hans Christian Řersted (1777-1851) noticed that a compass moves when it is brought near a wire carrying current. This was the first notion that electricity and magnetism are related. A wire that is carrying current will produce a circular magnetic field around the wire. When this current-carrying wire is subjected to an external magnetic field, a magnetic force is felt on the wire. The magnetic force is actually acting on the moving electrical charges (electrons) within the current-carrying wire.

Previous experiments used static electrical charges, but the use of moving electrical charges (current) was Řersted's breakthrough. The current in a wire is a movement of charges. It is actually the negatively charged electrons that move in a wire, but due to historical convention, the current is defined as the flow of positive charges.

When charged moving particles are placed in a magnetic field, they experience a magnetic force given by the Lorentz force equation. This states that the magnetic force felt by a charged particle is equal to the product of the charge of the particle, the velocity of the particle and the component of the velocity that is perpendicular to the magnetic field. The magnetic force is produced in a direction that is itself perpendicular to both the velocity and the magnetic field.

Since the current (I) is defined as the flow or number (n) of positive charges (q) passing through the area A of a wire, we can write equation of the current in a wire of cross-sectional area A as

I = n × g × v × A. If each of these charges experience a Lorentz force from a magnetic field we can write the equation for the magnetic force on a length of wire L asThe vectoris known as a vector cross-product, a vector that has a magnitude , where is the angle between vectors L and B.

The right-hand rule is a useful tool for finding the direction of a cross-product. There are a number of ways to use this tool. One way is to point your fingers in the direction of the current I, and then curl your fingers in the direction of the external magnetic field (B). Your thumb will point in the direction of the magnetic force. The magnitude of the magnetic force we can now write as This equation is a simplified version of the Lorentz force on a length of current-carrying wire. We can see that the magnetic force (F) is directly proportional to the current (I) length of wire (L) in the external magnetic field, the external magnetic field magnitude (B), and the sine of the angle , between the current direction in the wire and the external magnetic field. Because of this, the magnetic force is greatest if the current direction in the wire is perpendicular to the external magnetic field and zero when it is parallel to the external magnetic field.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should be able to define electric current, properties of force as a vector quantity, electric charge, magnetic poles; determine the direction and magnitude of a magnetic field of a straight current-carrying wire,
Course Physics
Type of Tutorial Concept Development
Key Vocabulary charges, currents, current carrying wires