Physics 30 Lesson 21: The Motor Effect

Physics 30 Lesson 21: The Motor Effect

I. Current Carrying Wires in External Magnetic Fields

  • When a charged particle enters an external magnetic field, it experiences a force that is perpendicular to its line of motion.

  • A similar effect occurs with current-carrying wires placed in external magnetic fields.

  • The interaction between the induced magnetic field around a current-carrying wire and the external magnetic field results in a force.

Direction of the Force

  • To determine the direction of the force $(F)$ on a current carrying wire in an external magnetic field $(B)$, we apply the third hand rule (Right Hand Rule):

    • Fingers point in the direction of the external magnetic field $(B)$.

    • Thumb points in the direction of the current (use right hand for conventional current, left hand for electron flow).

    • Palm indicates the direction of the force $(F)$ on the wire.

Examples

  • Example 1: If the electron flow is into the page:

    • Using the left hand: Fingers point right ($B$), thumb points into the page (electron flow), palm indicates force direction is up the page.

  • Example 2: If electrons flow from A to B in the conductor:

    • Using the left hand: Fingers point left ($B$), thumb points down the page (electron flow), palm indicates force is out of the page.

  • Example 3: Determining the current direction when a conductor is forced up out of the page:

    • Fingers point left ($B$), palm faces the observer, so the current flows from B to A (conventional current).

II. Magnitude of the Deflecting Force on a Conductor

  • To derive the magnetic force equation for a conductor:

    • Previously derived equation for deflecting force on a charged particle in a magnetic field: F = qvB ext{sin} heta where:

      • $F =$ deflecting force (N)

      • $q = $ charge (C)

      • $v = $ speed of the charged particle (m/s)

      • $B = $ magnetic field strength (T)

      • $ heta = $ angle between particle's velocity and the magnetic field direction.

Force on a Conductor

  • When substituting for current $(I)$ and length $(L)$: F = BIL ext{sin} heta

    • Where:

    • $B =$ magnetic field strength (T)

    • $I =$ current (A)

    • $L =$ length of wire within the magnetic field (m)

    • $ heta = $ angle between the current and the magnetic field.

  • Maximum deflecting force occurs when $ heta = 90°$.

Example 4

  • A 5.0 cm wire experiences a force of 0.023 N in a 1.25 T magnetic field:

  • Calculate the current:
    F = BIL
    Rearranging yields:
    I = rac{F}{BL}
    Substituting known values:
    I = rac{0.023 ext{ N}}{1.25 ext{ T} imes 0.050 ext{ m}} = 0.37 ext{ A} ext{ to the right}

  • Example 5: A 25 cm wire at 30° angle with a current of 0.75 A produces a 2.6 μN force:

    • Rearranging magnetic force equation yields:
      B = rac{F}{I imes L imes ext{sin} heta}

III. The Current Balance

  • The current balance is a device that demonstrates the deflecting force of a current-carrying wire in an external magnetic field.

  • It consists of a rectangular piece of wood with wire around half its perimeter.

  • The ends of the wire act as a fulcrum; an external magnetic field is supplied by a solenoid.

Operational Principle

  • Known weights are added to one end of the balance, applying current through the conductor until gravitational force is balanced by the magnetic force:
    Fg = Fm

  • Only sections of wire perpendicular to the magnetic field produce a magnetic force; sections parallel do not contribute to the force.

IV. Electric Motors

  • Following Oersted's discovery of electromagnetism, Ampere analyzed the magnetic effect on current-carrying wires.

  • He studied how induced magnetic fields around wires create repulsive or attractive forces, leading to the definition of the ampere based on force.

Faraday's Contributions

  • Michael Faraday derived the first electric motor concept through his electromagnetic rotator in 1821, having two main designs:

    • A bar magnet rotates around a fixed current.

    • A rod carrying current rotates around a fixed magnet.

  • Enhancements to the electric motor were made to effectively convert electric energy into mechanical energy.

V. Practice Problems

  1. Predict direction of movement for current flowing from A to B.

  2. Determine the direction of conventional current if the resulting force moves to the right.

  3. Given a 10 cm wire with 20 A current in a 2.0 T field, find the deflecting force $(F=4.0 ext{ N into page})$.

  4. Determine deflecting force on a 40 cm conductor in a 0.50 T field at 60° angle with 20 A current $(F=3.5 ext{ N})$.

VI. Hand-in Assignment

  1. Direction of deflecting force for alpha particles in a downwards field.

  2. Correct units for magnetic flux density from available units.

  3. Find the magnitude and direction of the force on a 40 m conductor with 80 A current in Earth’s magnetic field.

  4. Determine current in a horizontal conductor in a field balancing gravitational force $(I = 5.5 A)$.