Bar magnet P is twice as strong as bar magnet Q.
(a) The two magnets are arranged with the N-pole of P 1 metre from the S-pole of Q.
Is there a neutral point between the two magnets? If there is, how far from magnet P is it located?
If there is no neutral point, explain why.
Yes, there is a neutral point between the two magnets. The neutral point is located closer to the weaker magnet Q. This is because the strength of magnet P is twice that of magnet Q. The distance from magnet P to the neutral point can be calculated by equating the magnetic forces exerted by the two magnets on a hypothetical unit N pole placed between them.
Let the distance from magnet P to the neutral point be x metres.
According to inverse square law, the magnetic force exerted by magnet P on the unit N pole is proportional to 1/(1^2+x^2), and the force exerted by magnet Q is proportional to 1/(1^2+(1-x)^2).
Since magnet P is twice as strong as magnet Q, the forces can be equated as follows:
1/(1^2+x^2) = 2 * 1/(1^2+(1-x)^2)
1/(1+x^2) = 2/(2-x)^2
2(1+x^2) = (2-x)^2
2 + 2x^2 = 4 - 4x + x^2
x^2 + 4x - 2 = 0
x = (-4 + sqrt(16 + 8))/2
x = (-4 + sqrt(24))/2
x = (-4 + 4.899)/2
x = 0.449 metres
Therefore, the neutral point is located 0.449 metres from magnet P.
There is a neutral point between the two magnets because the magnetic forces exerted by the two magnets on a unit N pole cancel each other out at this point. This is possible due to the inverse square law, which governs the strength of magnetic forces between magnets at different distances.