Simulation · Physics · Class 12

Field on the axis and on the equator

From the lesson The electrostatic analog in Magnetism and Matter. Change the values and watch what happens.

Field on the axis and on the equatorPhysics · Class 12

The idea behind it

NCERT §5.2.4

The far field of a bar magnet of moment m follows from the electric dipole's field by swapping E → B, p → m and 1/(4πε₀) → μ₀/4π.
On the axis, at distance r much larger than the magnet's size l: B_A = (μ₀/4π)(2m/r³), along m.
On the equatorial line (the normal bisector), for r ≫ l: B_E = −(μ₀/4π)(m/r³), half the axial size at the same distance and pointing opposite to m.
Both fall off as 1/r³: doubling the distance cuts the field to one-eighth.
The dipole analogy runs through the table: 1/ε₀ ↔ μ₀, p ↔ m, torque p × E ↔ m × B, energy −p·E ↔ −m·B.
Example 5.2: a needle Q near a needle P is in equilibrium only when m_Q is parallel or antiparallel to P's field at Q. Parallel is stable, antiparallel unstable, and the lowest energy comes with Q on P's axis, pointing along P's field there, where that field is twice its equatorial size.