Question

The magnitude of the magnetic field B a distance r from a long straight wire is B = μ 0 I 2 π r where μ 0 is the permeability constant of free space, and I the current in the wire. The magnetic field is measured at four different distances from a long straight wire while the current is held constant. Order the magnitudes of the measured magnetic field at each distance, from lowest to highest.

Answer 1

The magnetic field is lowest for largest distance and highest when distance is least.

Step-by-step explanation:

The magnitude of magnetic field strength at a distance 'r' from a long straight wire carrying current 'I' is given as:

`B=(\mu_0 I)/(2\pi r)\\Where,\mu_0\to permeability\ constant\ of\ free\ space`

Now, as per question, the distance 'r' is varied while keeping the current constant in the wire.

As seen from the above formula, the magnitude of magnetic field strength for a constant current varies inversely with the distance 'r'. This means that, as the value of 'r' increases, the magnitude of magnetic field strength decreases and vice-versa.

Therefore, the magnitude of magnetic field strength is maximum when the distance 'r' is least and the magnetic field is minimum for the largest distance.

Example:

If
`B_1, B_2,\ and\ B_3` are the magnitudes of magnetic field strengths for distances
`r_1,r_2, \ and\ r_3` respectively such that
`r_1<r_2<r_3`. Now, as per the explanation above, the order of magnitudes of magnetic field strength is:

`B_1>B_2>B_3`