Question

A 2.00-m lamp cord leads from the 110 V outlet to a lamp having a 75.0 Wlightbulb. The cord consists of two insulated parallel wires 4.00 mm apart and held together by the insulation. One wire carries the current into the bulb and the other carries it out. What is the magnitude of the magnetic field the cord produces:

a) Midway between the two wires

b) At a point 2.00 mm from one of the wires in the same plane which the two wires lie (but on the opposite side)?

c)Compare each of the fields in parts a) and b) with the magnitude of the Earth’s magnetic field (0.5*10^-4 T ).

d)What magnetic force (magnitude and direction) do the two wires exert on one another?Is the force large enough to stress the insulation holding the wires together?

Answer 1

The magnitude of the magnetic field produced by the cord can be calculated using Ampere's Law. The magnetic field is different at different points relative to the wires. The wires exert a magnetic force on each other, which can be calculated using the formula for the force between two parallel conductors.

Step-by-step explanation:

The magnitude of the magnetic field produced by the cord can be calculated using Ampere's Law, which states that the magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

a) To find the magnitude of the magnetic field midway between the two wires, we can assume that the wires are carrying the same current in opposite directions. Using the formula B = (u0 * I) / (2 * pi * r), where B is the magnetic field, u0 is the permeability of free space, I is the current, and r is the distance, we can calculate the magnetic field.

b) To find the magnitude of the magnetic field at a point 2.00 mm from one of the wires on the opposite side, we can assume that only one wire is carrying the current. Using the same formula as above, we can calculate the magnetic field.

c) To compare the magnetic fields in parts a) and b) with the magnitude of the Earth's magnetic field (0.5*10^-4 T), we simply compare the values.

d) The two wires exert a magnetic force on each other due to their currents. The magnitude and direction of this force can be calculated using the formula F = (u0 * I1 * I2 * L) / (2 * pi * d), where F is the force, u0 is the permeability of free space, I1 and I2 are the currents in the wires, L is the length of the wires, and d is the distance between them. By comparing the magnitude of the force with the strength of the insulation holding the wires together, we can determine if the force is large enough to stress the insulation.