Answer:
a) Magnitude of the magnetic field midway between the two wires = 0.0000682 T = (6.82 × 10⁻⁵) T
b) Magnitude of the magnetic field the cord produces 2.0 mm from one of the wires in the same plane in which the two wires lie
= 0.00009093 T = (9.093 × 10⁻⁵) T
c) B(earth) = (0.5×10⁻⁴) T
B(a) = Magnetic field midway between the wires = (6.82 × 10⁻⁵) T
B(b) = Magnetic field at a point 2 mm from one of the wires = (9.093 × 10⁻⁵) T
Both magnetic fields exceed the earth's magnetic field.
(Ba/Bearth) = 1.364
(Bb/Bearth) = 1.8186
Explanation:
First of we obtain the current in the wires.
P = IV
I = (P/V) = (75/110) = 0.682 A
Magnetic field at a distance from a current carrying wire is given as
B = μ₀I/2πr
if two wires carry current in opposite direction, the magnetic field produced between them is the sum of the individual magnetic field due to each wire.
B = [μ₀I₁/2πr] + [μ₀I₂/2πr]
μ₀ = magnetic constant = (4π × 10⁻⁷) H/m
I₁ = current in wire 1 = 0.682 A
I₂ = current in wire 2 = 0.682 A
r = distance at which we want to evaluate the magnetic field due to the current in the wires = (8mm/2) = 4 mm = 0.004 m
I₁ = I₂ = 0.682 A
B = 2[μ₀I/2πr] = [μ₀I₁/πr]
B = (4π × 10⁻⁷× 0.682)/(π×0.004)
B = 0.0000682 T = (6.82 × 10⁻⁵) T
b) magnitude of the magnetic field the cord produces 2.0 mm from one of the wires in the same plane in which the two wires lie
B = [μ₀I₁/2πr₁] + [μ₀I₂/2πr₂]
μ₀ = magnetic constant = (4π × 10⁻⁷) H/m
I₁ = current in wire 1 = 0.682 A
I₂ = current in wire 2 = 0.682 A
r₁ = distance at which we want to evaluate the magnetic field due to current in wire 1 = 2mm = 0.002 m
r₂ = distance at which we want to evaluate the magnetic field due to the current in the wire 2 = 8 mm - 2 mm = 6 mm = 0.006 m
I₁ = I₂ = 0.682 A
B = [μ₀I/2π] [(1/r₁) + (1/r₂)]
B = [4π × 10⁻⁷ × 0.682/2π] [(1/0.002) + (1/0.006)]
B = (1.364 × 10⁻⁷) [666.6667] = 0.00009093 T = (9.093 × 10⁻⁵) T
c) Compare the field between the two wires with Earth’s magnetic field (0.5×10⁻⁴ T). Give your answer as B/BEarth.
The two fields obtained in (a) and (b) above, are both more than the earth's magnetic field.
B(earth) = (0.5×10⁻⁴) T
B(a) = Magnetic field midway between the wires = (6.82 × 10⁻⁵) T
B(b) = Magnetic field at a point 2 mm from one of the wires = (9.093 × 10⁻⁵) T
(Ba/Bearth) = (6.82 × 10⁻⁵)/(0.5×10⁻⁴) = 1.364
(Bb/Bearth) = (9.093 × 10⁻⁵)/(0.5×10⁻⁴) = 1.8186
Hope this Helps!!!
