91影视

• Figure of three circuits in which R > r.
• Same current is flowing through each circuit and the angle between two radial lengths is the same.

Find the net magnetic field at the center of each circuit using the formula for the magnetic field at the center of a circular loop. Rank the givencircuits according to the magnitude of the magnetic field at the center.

The expression for magnetic flux density is given by,

$B=\frac{{渭}_{0}if}{4蟺R}$

Where, B is magnetic field, R is radius, iis current,饾泹is permeability.

The magnitude of the magnetic field at the center of the arc is given by,

$B=\frac{{渭}_{0}if}{4蟺R}$

The net magnetic field at the center of circuit (a) is,

$B=\frac{{渭}_{0}i\left(2蟺-f\right)}{4蟺R}+\frac{{渭}_{0}if}{4蟺r}$

The net magnetic field at the center of the circuit (b) is,

$B=\frac{{渭}_{0}if}{4蟺r}-\frac{{渭}_{0}if}{4蟺R}$

The net magnetic field at the center of circuit (c) is,

$B=\frac{{渭}_{0}i\left(2蟺-f\right)}{4蟺r}+\frac{{渭}_{0}if}{4蟺R}$

Since, $R>randf鈮�2蟺鈭�f$, the ranking of circuits according to the magnitude of the net magnetic field at the center is,

c > a > b

Hence, the circuits according to the magnitude of the net magnetic field at the center, greatest first is c > a > b.

Therefore, the magnetic field at the center of arc depends inversely on its radius.