Question:
The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r (r >> L)$
The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r (r >> L)$
Updated On: May 29, 2024
- decreases as $\frac{1}{r}$
- decreases as $\frac{1}{r^{2}}$
- decreases as $\frac{1}{r^{3}}$
- approaches a finite limit as $r \to \infty$
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The Correct Option is B
Solution and Explanation
By Biot-Savart's law, the magnetic field due to a current carrying wire is
$B=\frac{\mu_{0}}{4 \pi} \cdot \frac{I d l \sin \theta}{r^{2}}$
So, $B \propto \frac{1}{r^{2}}$
So, the magnetic field due to current decreases as inverse square of distance of the point of observation.
$B=\frac{\mu_{0}}{4 \pi} \cdot \frac{I d l \sin \theta}{r^{2}}$
So, $B \propto \frac{1}{r^{2}}$
So, the magnetic field due to current decreases as inverse square of distance of the point of observation.
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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.