# Biot-Savart Law

If the current is given, we use this form $dB=4πμ_{0} r_{2}Idl×r^ $

We can then integrate $dB$ to find $B$.

- $r$ is a unit vector that always points from A (the charge) to P (where we are measuring the magnetic field)

Approach, pretty straightforward. The calculations are similar for Electric Field Calculations

- Find the current $I$
- Find $∣dl×r∣$, see Cross Product
- Find $r$

### Biot-Savart for moving charges

If velocity is given, we replace $I=dtdq $ we use this form $dB=4πμ_{0} dqr_{2}v×r^ $

### More details

To master this, you really just need to do lots of exercises.

Notice the placement of $θ$ in these problems. You tend to place the angle $θ$ next to $dB$ and then think of ways, but make your life easier by placing theta like in the picture. Then say, for the z axis, it’s using a $cos$, so you can just do the opposite, therefore $dB_{z}=dBsinθ$

Solving Solenoid Problem