a) Find the forces per unit length on two long, straight and parallel conductors, if each carries a current of 10.0 A in the same direction and the separation distance is 0.20 m.
b) Find the maximum torque on an 85-turn, rectangular coil, 0.2 m by 0.3 m, carrying a current of 2.0 A in a field B =6.5 T.
3.
To find the forces per unit length on two long, straight, and parallel conductors, we can use Ampere's Law. Ampere's Law states that the magnetic field created by a long, straight conductor is directly proportional to the current and inversely proportional to the distance from the conductor.
a) The formula to find the magnetic field created by a current-carrying conductor is given by:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field
μ₀ is the permeability of free space (μ₀ = 4π × 10^-7 Tm/A)
I is the current
r is the separation distance between the conductors
Since we have two parallel conductors carrying the same current in the same direction, the forces per unit length can be found using the formula:
F = (μ₀ * I₁ * I₂) / (2π * r)
Where:
F is the force per unit length
μ₀ is the permeability of free space
I₁ and I₂ are the currents in the two conductors
r is the separation distance between the conductors
Plugging in the given values:
I₁ = I₂ = 10.0 A
r = 0.20 m
μ₀ = 4π × 10^-7 Tm/A
F = (4π × 10^-7 Tm/A * 10.0 A * 10.0 A) / (2π * 0.20 m)
F = 2 × 10^-6 N/m
Therefore, the forces per unit length on the two conductors is 2 × 10^-6 N/m.
b) To find the maximum torque on a rectangular coil, we can use the formula:
τ = N * B * A * I * sin(θ)
Where:
τ is the torque
N is the number of turns in the coil
B is the magnetic field
A is the area of the coil
I is the current
θ is the angle between the magnetic field and the normal to the coil
Plugging in the given values:
N = 85 turns
B = 6.5 T
A = 0.2 m * 0.3 m = 0.06 m²
I = 2.0 A
θ is not given, assuming it's 90 degrees for maximum torque (sin(90) = 1)
τ = 85 * 6.5 T * 0.06 m² * 2.0 A * 1
τ = 663 Nm
Therefore, the maximum torque on the rectangular coil is 663 Nm.