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

Answer:

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

Explanation:

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

$B=\frac{\mu_0 I}{2\pi r}\\Where,\mu_0\to permeability\ constant\ of\ free\ space$

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:

$B_1>B_2>B_3$