Question:
Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20\, cm$ and $40\, cm$ and carry $0.2\, A$ and $0.3\, A$. current respectively in opposite directions. The magnetic induction (in tesla) at the center is
Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20\, cm$ and $40\, cm$ and carry $0.2\, A$ and $0.3\, A$. current respectively in opposite directions. The magnetic induction (in tesla) at the center is
Updated On: Jan 30, 2025
- $\frac{3}{4} \mu_0$
- $\frac{5}{4} \mu_0$
- $\frac{7}{4} \mu_0$
- $\frac{9}{4} \mu_0$
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The Correct Option is B
Solution and Explanation
Two coils carry currents in opposite directions, hence net magnetic field at center will be difference of the two fields.
ie, $B_{net}=\frac{\mu_{0}}{4 \pi} \cdot 2 \pi N \frac{i_{1}}{r_{1}}-\frac{i_{2}}{r_{2}}$
$=\frac{10 \mu_{0}}{2} \frac{02}{02}-\frac{0.3}{0.4}$
$=\frac{5}{4} \mu_{0}$
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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.