Magnetism and Magnetic Materials

Dr. Reinhard K. Kremer Magnetism and Magnetic Materials Brock University Course No. PHYS 5P74 (2014) 1st Homework Assignment (due Monday May 12, 2014) 1. Some vector calculus (a) The scalar triple product Without expanding the vector into their components show that ABC (b) Prove that for any vectors A, B, C A  (B  C) = (AC) B – (AB) C (c) Using the results of (a) and (b) to prove the relation (AB)  (PQ) = (AP) (BQ) – (AQ) (BP) 2. Vector potential Show that the vector potential A   r H 2 1 indeed gives the uniform field H . 3. Magnetic Field on the symmetry axis of a circular coil Consider a short circular coil of length L with N turns with radius  which is charged with a current I. Calculate the magnetic field H by using the BIOT-SAVART for an arbitrary point on the symmetry axis of the coil. Hint: Calculate the field for a single turn first and superpose the solution. BIOT-SAVART’s law: ( dl  is an infinitesimal small segment of a turn carrying the current I . r is the distance from this element to the point P for which you want to calculate the field H. from this element to the point P for which you want to calculate the field H. 4. HELMHOLTZ coil Combine two single coils each with N turns and form a HELMHOLTZcoil by putting them at a distance r, where r is the radius of each single coil. What is the advantage of putting the two coils at a distance r? (Hint: Calculate the variation of the field on the symmetry axis at midpoint, homogeneity). 2 ˆ 4 r I dl r dH      