Magnetic flux and magnetic field at a point are related concepts in electromagnetism, but they are fundamentally different. Below is the concise differentiation:
| Magnetic Flux | Magnetic Field at a Point |
|---|---|
| Scalar quantity | Vector quantity |
| \( \Phi_B = B A \cos \theta \) | \( \mathbf{B} = \frac{F}{qv} \) |
| Measured in Weber (Wb) | Measured in Tesla (T) |
| Depends on area | Depends on current and distance |
| Total number of field lines through a surface | Local property of space at a point |
In summary, magnetic flux is the total magnetic field passing through a given area, while the magnetic field at a point refers to the local magnetic influence at a specific point in space.
A short bar magnet placed with its axis at 30º with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10-2 J. What is the magnitude of magnetic moment of the magnet?
A short bar magnet of magnetic moment m = 0.32 J T-1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its ( a ) stable, and ( b) unstable equilibrium? What is the potential energy of the magnet in each case?
A closely wound solenoid of 800 turns and area of cross section 2.5 × 10-4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?