Applied Electricity and Magnetism ECE 3318 Applied Electricity and Magnetism Spring 2017 Prof. David R. Jackson ECE Dept. Notes 29

Biot-Savart Law a) Volume current b) Surface current r Please see the textbooks for a derivation. a) Volume current b) Surface current r

Biot-Savart Law (cont.) c) Line current (wire) Note on notation: Rule: The contour C is in direction of the I arrow (i.e., the reference direction for the current). (This determines the starting point A and the ending point B.)

Example Find H Infinite line current

Example (cont.) Hence we have:

Example (cont.) I

Example (cont.) Note: Hence we have or

Example (cont.) Summary Note: This agrees with the answer obtained by Ampere’s law.

Example Find H Circular loop of current Note: This problem cannot be solved using Ampere’s law!

Example (cont.) so

A prime is not necessary on unit vector z. Example (cont.) Note: A prime is not necessary on unit vector z. so

Example (cont.) Summary x y z a r = (0,0,z) I

Example (cont.) r = (0,0,z) As z  : I z a y x This explains why it is difficult to achieve a significant range in a wireless charging system: