a. What current is flowing in a 2.0m length of wire in the Earth's field of 55μT if it experiences a force of 10mN?
b. A 2 wire cable is suppling 100 A to a DC motor. Each wire has a 2 mm insulation layer and there is also a 2 mm separate insulation layer between the 2 wires. What is the force between the 2 conductors? Does these conductors repelled or attracted by that force?
c. Determine the m.m.f. necessary to create a flux of 0.5 Weber in a magnetic core which has a reluctance of 100 At/Wb.
d. A current balance has a 5.0 cm wide arm between the poles of a magnet. The flux density, B, between the poles is measured as 25mT. When the current is 1.5A, what is the force on the arm?
a. To find the current flowing in the wire, we can use the equation for the force experienced by a current-carrying wire in a magnetic field:
F = BIL
Where F is the force, B is the magnetic field strength, I is the current, and L is the length of the wire. Rearranging the equation to solve for the current:
I = F / (BL)
Given that the force F is 10mN, the magnetic field strength B is 55μT (convert to Tesla by dividing by 10^6), and the length L is 2.0m, we can substitute these values into the equation:
I = (10 x 10^-3 N) / ((55 x 10^-6 T) x (2.0 m))
Simplifying the equation:
I = 0.909 A
Therefore, the current flowing in the wire is approximately 0.909 Amperes.
b. To find the force between two conductors in a cable carrying a current, we can use the equation for the force per unit length between two parallel conductors:
F = (μ0 * I1 * I2 * L) / (2πd)
Where F is the force, μ0 is the permeability of free space (4π x 10^-7 Tm/A), I1 and I2 are the currents in the two wires, L is the length of the wires, and d is the distance between the wires. Rearranging the equation to solve for the force:
F = (μ0 * I1 * I2 * L) / (2πd)
Given that the two wires have a current of 100A and there is a 2mm (convert to meters) insulation layer between the wires, we can substitute these values into the equation:
F = (4π x 10^-7 Tm/A) * (100A) * (100A) * (L) / (2π * 2mm)
Simplifying the equation:
F = (2 x 10^-7 N/m^2) * (10^4 A^2) * (L) / (d)
Therefore, the force between the two conductors is directly proportional to the length of the wires and inversely proportional to the distance between the wires.
To determine whether the conductors are repelled or attracted by that force, we need to consider the direction of the current in each wire. If the currents flow in the same direction, the conductors will be attracted to each other. If the currents flow in opposite directions, the conductors will be repelled from each other.
c. To determine the magnetomotive force (mmf) necessary to create a flux in a magnetic core, we can use the equation for mmf:
N = Φ / R
Where N is the mmf, Φ is the flux, and R is the reluctance. Rearranging the equation to solve for mmf:
N = Φ / R
Given that the flux Φ is 0.5 Weber and the reluctance R is 100 At/Wb, we can substitute these values into the equation:
N = (0.5 Wb) / (100 At/Wb)
Simplifying the equation:
N = 0.005 A
Therefore, the magnetomotive force necessary to create a flux of 0.5 Weber in a magnetic core with a reluctance of 100 At/Wb is 0.005 Ampere-turns.
d. To find the force on the arm of a current balance, we can use the equation for the force experienced by a current-carrying wire in a magnetic field:
F = BIL
Where F is the force, B is the flux density, I is the current, and L is the length of the wire. Given that the width of the arm is 5.0 cm (convert to meters), the flux density B is 25mT (convert to Tesla by dividing by 10^3), and the current I is 1.5A, we can substitute these values into the equation:
F = (25 x 10^-3 T) * (1.5 A) * (5.0 x 10^-2 m)
Simplifying the equation:
F = 1.875 x 10^-3 N
Therefore, the force on the arm is approximately 1.875 millinewtons.