Question:
A short bar magnet has a magnetic moment of $0.48\, J\, T^{-1}$. The magnitude and direction of magnetic field produced by the magnet at a distance of $10 \,cm$ from the centre of the magnet on its axis is
A short bar magnet has a magnetic moment of $0.48\, J\, T^{-1}$. The magnitude and direction of magnetic field produced by the magnet at a distance of $10 \,cm$ from the centre of the magnet on its axis is
Updated On: Sep 26, 2023
- $0.48 \times 10^{-4}\, T$ along $N-S$ direction
- $0.28 \times 10^{-4}\, T$ along $S-N$ direction
- $0.28 \times 10^{-4}\, T$ along $N-S$ direction
- $0.96 \times 10^{-4}\, T$ along $S-N$ direction
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The Correct Option is D
Solution and Explanation
On the axis of the magnet
$B = \frac{\mu_{0}}{4\pi} \cdot \frac{2m}{d^{3}}$
Here, $\frac{\mu _{0}}{4\pi } = 10^{-7} \, A\,m^{-2}$
$m = 0.48 \,J \,T^{-1}, d = 10 \,cm = 0.1 \,m$
Then, $B = \frac{10^{-7}\times 2 \times 0.48 }{\left(0.1\right)^{3}}$
$= 0.96 \times 10^{-4}\,T$, along $S-N$ direction.
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.