Question:
Two concentric circular coils, each having 10 turns with radii 0.2 m and 0.4 m carry currents 0.2 A and 0.3 A respectively in opposite directions. Magnetic field at the centre is
Two concentric circular coils, each having 10 turns with radii 0.2 m and 0.4 m carry currents 0.2 A and 0.3 A respectively in opposite directions. Magnetic field at the centre is
Updated On: Aug 1, 2022
- $(2 / 3) \, \mu_0 $
- $(5 / 4) \, \mu_0 $
- $(1 / 4) \, \mu_0 $
- $(1 / 6) \, \mu_0 $
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The Correct Option is B
Solution and Explanation
Here, $r_1 = 0.2 \, m$,
$ r_2 = 0.4 \, m$,
$ I_1 = 0.2 \, A$,
$I_2 = 0.3 \, A$
$n_1 = n_2 = n = 10$
Magnetic field due to smaller loop at the centre $O$,
$\bar{B}_1 = \frac{ n \mu_0 I_1}{2 r_1}\bigotimes $
$ = \frac{10 \times \mu_0 \times 0.2}{2 \times 0.2} = 5 \mu \bigotimes$
Magnetic field due to larger loop at centre $O$,
$\bar{B}_2 = \frac{ n \mu_0 I_2}{2 r_1} \bigodot $
$ = \frac{10 \times \mu_0 \times 0.3}{2 \times 0.4} = \frac{15}{4} \mu \bigodot$
Net magnetic field at the centre,
$\bar{B}_0 = \bar{B}_1 - \bar{B}_2$
$ = 5 \mu_0 - \frac{15}{4} \mu_0 = \frac{5 \mu_0}{4}$
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.