Question:
A compass needle whose magnetic moment is $60\, A \,m^2$ pointing geographical north at a certain place where the horizontal component of earth?s magnetic field is $40 \times 10^{-6}\, Wb\, m^{-2}$ experiences a torque of $1.2 \times 10^{-3}\, N\, m$. The declination of the place is
A compass needle whose magnetic moment is $60\, A \,m^2$ pointing geographical north at a certain place where the horizontal component of earth?s magnetic field is $40 \times 10^{-6}\, Wb\, m^{-2}$ experiences a torque of $1.2 \times 10^{-3}\, N\, m$. The declination of the place is
Updated On: Jun 23, 2023
- $20^{\circ}$
- $45^{\circ}$
- $60^{\circ}$
- $30^{\circ}$
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The Correct Option is D
Solution and Explanation
In stable equilibrium, a compass needle points along magnetic north and experiences no torque.
When it is turned through declination $\alpha$, it points along geographic north and experiences torque,
$\tau = mB \,sin\alpha$
$\therefore\quad sin\,\alpha = \frac{\tau}{mB} $
$= \frac{1.2 \times 10^{-3}}{60 \times 40 \times 10^{-6}} $
$= \frac{1}{2}$ or $\alpha = 30^{\circ}$
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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.