Question

Two short magnets of magnetic moment 1000 $Am^2$ are placed as shown at the corners of a square of side 10 cm. The net magnetic induction at $P$ is

Answer 1

Cannot be answered without the figure.

Answer 2

The problem states that "Two short magnets of magnetic moment 1000 Am² are placed as shown at the corners of a square of side 10 cm. The net magnetic induction at P is". However, the crucial figure showing the arrangement of the magnets and the location of point P is missing.

Without the diagram, it is impossible to definitively solve the problem, as the magnetic field depends critically on the positions and orientations of the magnets relative to point P.

Common Scenarios (and why they cannot be assumed without the figure):

1. Magnets at adjacent corners, P at the fourth corner: This would involve one magnet's field being calculated axially and the other's field requiring a general formula for a short magnet, leading to complex vector addition.
2. Magnets at opposite corners, P at the center: If the magnets are oriented along the diagonals and pointing towards the center, their fields would be equal in magnitude and opposite in direction, leading to a net field of zero. If they are oriented along the axes, the calculation becomes more involved.
3. Magnets at adjacent corners, P at the center: This would also involve complex vector addition unless specific orientations are given.

Given the standard nature of competitive exams, if a figure is implied but missing, the problem often refers to a configuration that results in a relatively straightforward calculation, or a specific value that is commonly asked.

Conclusion: The problem cannot be solved without the accompanying diagram showing the arrangement of the two short magnets and the position of point P. The phrase "as shown" explicitly indicates the necessity of a figure.

Therefore, I cannot provide a numerical solution.

Explanation of the solution (if the diagram were available):

1. Identify the positions of the magnets and point P: From the diagram, determine the coordinates of the two magnets and point P.
2. Determine the orientation of each magnet: The diagram would show the direction of the magnetic moment (from South to North pole) for each magnet.
3. Calculate the magnetic field due to each magnet:
   • For a short bar magnet, the magnetic field at a point depends on whether the point is on the axial line or equatorial line, or a general position.
   • The formula for magnetic field on the axial line is $B_{axial} = \frac{\mu_0}{4\pi} \frac{2M}{r^3}$, directed along the magnetic moment.
   • The formula for magnetic field on the equatorial line is $B_{equatorial} = \frac{\mu_0}{4\pi} \frac{M}{r^3}$, directed opposite to the magnetic moment.
   • For a general point at distance r and angle $\theta$ from the axis, $B = \frac{\mu_0}{4\pi} \frac{M}{r^3} \sqrt{1 + 3\cos^2\theta}$. The direction needs careful vector decomposition.
   • Given values: $M = 1000 \, \text{Am}^2$, side length $a = 10 \, \text{cm} = 0.1 \, \text{m}$.
   • Permeability of free space constant: $\frac{\mu_0}{4\pi} = 10^{-7} \, \text{T m/A}$.
4. Perform vector addition: Add the magnetic field vectors from each magnet at point P to find the net magnetic induction.

Without the diagram, this process cannot be completed.