Question
Discuss the magnetic field due to a current-carrying circular loop.###State the characteristics of the magnetic field produced by a current-carrying circular loop. Sketch its magnetic field lines.
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Answer
When a current is passed through a circular loop, a magnetic field is produced around it.
$\rightarrow$ The pattern formed by the magnetic field lines of the magnetic field due to a current-carrying circular loop is shown in figure 12.11.
$\rightarrow$ The magnetic field lines of the field produced by a current-carrying circular loop are circular and concentric near the loop.
$\rightarrow$ As we move away from wire, the concentric circles representing the magnetic field around it become larger and larger.
(The magnetic field is proportional to the current and decreases as we move away from the loop.)
$\rightarrow$ When we reach at the centre of the circular loop, the arcs of these big circles would appear as a straight line.
$\rightarrow$ Here every point on the circular wire carrying current would give rise to the magnetic field appearing as straight lines at the centre of the loop.By applying the Right-hand thumb rule, it can be seen that every section of the wire produces magnetic field/field lines in the same direction within the loop.
$\rightarrow$ Hence, at the centre of the circular loop, all the magnetic field lines are in the same direction and aid each other due to which the strength of the magnetic field increases.
$\rightarrow$ In case of a current-carrying circular coil having $N$ turns, the magnetic field produced is ' $N$ ' times as large as that produced by a coil having single turn, assuming that all turns have nearly the same radius.This is because the current in each circular turn has the same direction and the field due to each turn then just adds up.
$\rightarrow$ Thus, magnitude of the magnetic field $B$ produced at the centre of the coil is:
(1) Directly proportional to the current $I$ flowing through it, i.e., $B \propto I$
(2) Inversly proportional to the radius $r$ of the coil, i.e., $B \propto \frac{1}{r}$
(3) Directly proportional to the total number of turns $N$ of the coil, i.e., $B \propto N$
$\rightarrow$ The pattern formed by the magnetic field lines of the magnetic field due to a current-carrying circular loop is shown in figure 12.11.
$\rightarrow$ The magnetic field lines of the field produced by a current-carrying circular loop are circular and concentric near the loop.
$\rightarrow$ As we move away from wire, the concentric circles representing the magnetic field around it become larger and larger.
(The magnetic field is proportional to the current and decreases as we move away from the loop.)
$\rightarrow$ When we reach at the centre of the circular loop, the arcs of these big circles would appear as a straight line.
$\rightarrow$ Here every point on the circular wire carrying current would give rise to the magnetic field appearing as straight lines at the centre of the loop.By applying the Right-hand thumb rule, it can be seen that every section of the wire produces magnetic field/field lines in the same direction within the loop.
$\rightarrow$ Hence, at the centre of the circular loop, all the magnetic field lines are in the same direction and aid each other due to which the strength of the magnetic field increases.
$\rightarrow$ In case of a current-carrying circular coil having $N$ turns, the magnetic field produced is ' $N$ ' times as large as that produced by a coil having single turn, assuming that all turns have nearly the same radius.This is because the current in each circular turn has the same direction and the field due to each turn then just adds up.
$\rightarrow$ Thus, magnitude of the magnetic field $B$ produced at the centre of the coil is:
(1) Directly proportional to the current $I$ flowing through it, i.e., $B \propto I$
(2) Inversly proportional to the radius $r$ of the coil, i.e., $B \propto \frac{1}{r}$
(3) Directly proportional to the total number of turns $N$ of the coil, i.e., $B \propto N$
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