Question

A very long straight current-carrying wire produces a magnetic field of 20 mT at a distance d from the wire. To measure a field of 5 mT due to this wire, you would have to go to a distance from the wire of A very long straight current-carrying wire produces a magnetic field of 20 mT at a distance d from the wire. To measure a field of 5 mT due to this wire, you would have to go to a distance from the wire of:_____.

a. 4d.
b. 16d.
c. 2d.
d. 8d.

Answer 1

A. 4d

Step-by-step explanation:

Let's begin with the formula for the magnetic field produced by a long wire.

`B = (\mu_0I)/(2\pi d)`

So
`d=(\mu_0 I)/(2\pi B )`

at point d_{1} is

`d_(1)=(\mu_(0) i)/(2 \pi B_(1)) \\ (d_(1))/(d)=((\mu_(0) i)/(2 \pi B_(1)))/((\mu_(0) i)/(2 \pi B)) \\ d_(2)=d\left((B)/(B)\right) \\ =d\left(\frac{20 \mathrm{mT}}{5 \mathrm{mT}}\right) \\ =4 d`

Hence, option (A) is correct answer