# 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?

• 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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