Magnetostatics - magnetic fields produced by electric currents

1. What is the formula for the attractive force between two parallel conducting wires carrying currents?

F = µ0 I1 I1/2πr

2. What is the magnetic force equation for a charge moving with velocity v through a magnetic field B?

F = qv × B

3. What is the current density equation?

J = ρv

4. What is the equation for the current I?

I = ∫ J.dS

How can we calculate the drift speed of current-carrying electrons in a wire

The drift speed of current-carrying electrons in a wire can be calculated as v = I / (NeS), where N is the number of conduction electrons per unit volume of wire, e is the charge of an electron, and S is the uniform cross-sectional area of the wire

6. Why does the dependence on speed arise in electric and magnetic forces?

Electric and magnetic forces are manifestations of the same physical phenomenon, viewed from different frames of reference. The dependence on speed arises because of the phenomenon of Lorenz contraction.

7. What is Gauss's law for magnetic fields?

Gauss's law for magnetic fields states that the net magnetic flux coming out of a closed box is zero.

8. What is the divergence of the magnetic field?

The divergence of the magnetic field is given by ∇.B = 0.

9. What is Ampère's circuital law?

Ampère's circuital law states that the magnetic field integrated around a closed path is proportional to the current passing through the area enclosed by the path. ∮B.dl = µ0 I.

10. How can we calculate the magnetic field generated by a long straight wire carrying current I?

The magnetic field generated by a long straight wire carrying current I can be calculated using Ampère's law and the right-hand rule. B= ( µ0 I / 2πr) φ̂