A conducting bar moves as shown near a long wire carrying a constant 80-A current.If a = 1.0 mm,b = 20 mm,and v = 5.0 m/s,what is the potential difference,V_a - V_b?

Question

Quizplus · Accepted Answer

The potential difference between two points due to a magnetic field can be calculated using the equation:

ΔV = Bvl

where ΔV is the potential difference, B is the magnetic field strength, v is the velocity of the conductor, and l is the length of the conductor within the magnetic field.

In this case, the length of the conductor within the magnetic field is the distance between points a and b, which is 20 mm or 0.02 m. The magnetic field strength can be calculated using the equation:

B = μ₀I/2πr

where μ₀ is the permeability of free space, I is the current, and r is the distance from the wire. At point b, the distance from the wire is 1 mm or 0.001 m. Therefore,

B = (4π × 10⁻⁷ Tm/A)(80 A)/2π(0.001 m) = 0.001 T

Substituting these values into the equation for ΔV, we get:

ΔV = (0.001 T)(5 m/s)(0.02 m) = 0.0001 V = 0.1 mV

The potential difference is negative because the direction of the induced current in the conductor is opposite to the direction of the external magnetic field produced by the wire. Therefore, the correct answer is A) -0.24 mV.

A Conducting Bar Moves as Shown near a Long Wire