Question

Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction. What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?

Answer 1

The magnitude of the resulting magnetic field at a point that is 10 cm from each wire carrying a current of 20 A in the same direction is 16π x 10^-6 T.

Step-by-step explanation:

To calculate the magnitude of the resulting magnetic field at a point that is 10 cm from each wire, we can use the formula for the magnetic field produced by a long straight wire. This formula is given by:

B = (μ₀ * I) / (2π * r)

Where B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 T·m/A), I is the current in the wire, and r is the distance from the wire.

Using this formula for each wire, we can calculate the magnetic fields produced by them. Since the wires are carrying current in the same direction, the fields will add up. Therefore, the magnitude of the resulting magnetic field will be the sum of the magnetic fields produced by each wire.

Let's calculate:

B₁ (magnetic field produced by the first wire) = (4π x 10^-7 T·m/A * 20 A) / (2π * 0.1 m) = 8π x 10^-6 T

B₂ (magnetic field produced by the second wire) = (4π x 10^-7 T·m/A * 20 A) / (2π * 0.1 m) = 8π x 10^-6 T

The magnitude of the resulting magnetic field at a point that is 10 cm from each wire is the sum of B₁ and B₂:

B_resulting = B₁ + B₂ = 16π x 10^-6 T

Answer 2

B = 6.6825 ×
`10^(-5)` T

Step-by-step explanation:

Given that: I = 20 A, distance between the wires = 16 cm = 0.16 m, magnetic field at a point 10 cm (0.10 m) from each wire can be determined by;

The magnetic flux density (B) in a straight current carrying wire, is given as;

B =
`(U_(0)I )/(2\pi r)`

Where:
`U_(0)` is the permeability of free space = 1.26×
`10^(-6)` m kg/
`s^(2)`
`A^(-2)`, I is the current through the wires, r is the distance between the wires.

B = ( 1.26×
`10^(-6)` × 20) ÷ (2×
`(22)/(7)` × (0.16 - 0.10))

= 25.2 ×
`10^(-6)` ÷ 0.3771

B = 6.6825 ×
`10^(-5)` T