Physics · Magnetism And Matter · NEET
No. In a uniform field the north pole feels a force +mB in the field direction and the south pole feels an equal force mB in the opposite direction. These two equal and opposite forces cancel, so the net force is zero. The magnet only rotates (aligns with the field); its centre of mass stays put. It moves only in a non-uniform field.
Force adds up as a sum of the two pole forces: they are equal and opposite, so they cancel to zero. Torque depends on WHERE those forces act, not just their sum. The two opposite forces act at different points (the two poles), forming a couple. A couple gives no net force but a real turning effect, tau = mB sin theta. So force cancels while torque survives.
The gradient (rate of change) of the field along the magnet's axis. Net force F = m (dB/dx) when the dipole is aligned. If the field is stronger near the north pole than the south pole, the pole forces no longer cancel and a net pull toward the stronger-field region results (for a normal magnet or a paramagnet). A uniform field has dB/dx = 0, so F = 0.
A magnet, paramagnet or ferromagnet is pulled TOWARD the region of stronger field. A diamagnet is pushed toward the region of WEAKER field (repelled from the strong pole). This is exactly why an unmagnetised iron nail is attracted to a magnet: the nail becomes an induced magnet and is pulled into the stronger field.
Torque without net force: yes, in a uniform field (a pure couple). Net force without torque: yes, if the magnet is already aligned with a non-uniform field (theta = 0, so sin theta = 0 gives zero torque, but dB/dx is non-zero so force remains). In general non-uniform fields both act together.
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium. The energy required to rotate it by 60 degrees is W. The torque required to keep the magnet in this new (60 degrees) position is:
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current is switched on, the diamagnetic rod is pushed up, out of the horizontal magnetic field, gaining gravitational potential energy. The work required to do this comes from:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
tau = m B sin theta, where m is the magnetic moment, B is the field, and theta is the angle between m and B. In vector form tau = m x B. It is maximum at theta = 90 degrees and zero at theta = 0 (stable) or 180 degrees (unstable).
When the dipole is aligned with the field, the net force along the axis is F = m (dB/dx), the magnetic moment times the field gradient. If dB/dx = 0 (uniform field) the force is zero.
Yes. At theta = 0, sin theta = 0, so torque tau = mB sin 0 = 0. But in a non-uniform field a net force can still act even when torque is zero, because force depends on the field gradient, not on the angle.
The magnet's field near the nail is non-uniform. The nail becomes an induced magnet and, being ferromagnetic, is pulled toward the region of stronger field. This net force needs a field gradient, which is why the pull is stronger the closer the nail is.
In a uniform field, the restoring torque tau = mB sin theta (approx mB theta for small angles) makes a suspended magnet swing back and forth. That same torque gives the time period T = 2 pi sqrt(I / mB), the topic of the next page.
