Find pulling force and magnetic field?

Updated on August 6, 2022

A 8.00-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.330 Omega . Pulling the wire at a steady speed of 4.0 m/s causes 4.50 W of power to be dissipated in the circuit.

A) How big is the pulling force?

B) What is the strength of the magnetic field?

2 Answers

  • Let B = the magnetic field

    Let L = the length of the wire = 8.0 cm = 0.08 m

    Let R = the resistance of the wire = 0.330 Ω

    Let v = the velocity of the wire = 4 m/s

    Let E = the voltage across the wire

    Let P = the power of the wire = 4.5 W

    The power formula is:

    P = E²/R

    Solving for E:

    E = √{PR}

    The Voltage induced by a magnetic field is:

    E = vBL

    Use E = E:

    √{PR} = vBL

    Solving for B;

    B = √{PR}/vL

    B = √{4.5(0.33)}/(4)(.08)

    B = 3.8 Wb/m²

    Let F = the pulling force

    Let I = the current in the wire

    P = I²R

    I = √{P/R}

    F = IBL

    F = √{P/R}BL

    F = √{4.5/.33}(3.8)(.08)

    F = 1.12 N

  • A much simpler approach:

    Power=Force*velocity

    Force=power/velocity

    Force= 4.5(W) / 4(m/s)

    Force= 1.125 (Newtons)

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