Question

2) The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT. What is the magnetic field at a distance of 4 cm from the wire?

Answer 1

2 μT

Step-by-step explanation:

Assuming that the diameter of the current carrying wire is very small compared with its length, we can treat it as an infinite wire.

For an infinite wire, the magnetic field, at a distance r from the wire, is given by Biot-Savart law equation, as follows:

`B = (\mu0*I)/(2*\pi*r)`

where:

μ₀ = 4*π*10⁻⁷

I = current carried by the wire

r = distance from the wire.

So, B₁ can be calculated as follows:

`B1 = (\mu0*I)/(2*\pi*0.02m) = 4e-6 T`

If we change the distance where we want to know the value of B, all other factors remain constant, we can write the following expression for the new value of B, B₂:

`B2 = (\mu0*I)/(2*\pi*0.04m)`

Dividing B1 by B2, and simplifying common terms, we have:

`(B1)/(B2) = (0.04m)/(0.02m) = 2`

⇒
`B2 = (B1)/(2) = (4e-6T)/(2) = 2e-6 T`

⇒ B₂ = 2 μT