Question

The magnetic field 0.02 m from a wire is 0.1 T. What is the magnitude of the magnetic field 0.01 m from the same wire?

Answer 1

The magnetic field at 0.01m from the wire is 0.2T.

Step-by-step explanation:

The magnetic field
`B` at a distance
`R` due to a straight wire carrying a current
`I` is

`B = (\mu_oI )/(2\pi R),`

where
`\mu_o = 4\pi*10^(-7) m\cdot kg\cdot s^(-2) A^(-2)` is the magnetic constant.

Now, we are told that the magnetic field from a wire at
`R = 0.02m` is
`B = 0.01`; therefore,

`0.1T = ((4\pi*10^(-7))I )/(2\pi (0.02m)),`

solving for
`I` we get:

`I = 10,000A`

which is the current through the wire.

Now, the magnetic field
`B` of the wire due to this current at the distance of
`R = 0.01m` is

`B =((4\pi*10^(-7))(10,000))/(2\pi (0.01))`

`\boxed{B = 0.2 T}`

Thus, the magnetic field at 0.01m from the wire is 0.2T.