2) Ez = 1000 sin (20x - wt) find w and Bo. Write an equation for magnetic field

Example 1: A charge located at point (2,1,1) and the calculation point P is at (-1,2,2). Determine:- a. The distance between the charge and point P. b. The vector v xr when v = 2i – 3j + k. c. The magnetic flux density if v = -3j +k and q = 1 * 10-10 C. Example 2: Show that B = 0 if v = 3j + k and r = 12j + 4k.

6/6 points (graded) Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m2 /C2. vacuum permitivity, Eg = 8.854 x 10 12 F/m. Magnetic Permeability of vacuum, uo = 12.566370614356 x 10 7 H/m. Magnitude of the Charge of one electron, e = -1.60217662 x 10 19 C. Mass of one electron, m, = 9.10938356 x 10-31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, uC means micro coulomb The coordinate of the two charges q and q2 are given by (27, 33) and (18, 43). These coordinates are in nano meters. I component of the position vector q Give your answer up to at least three significance digits. 0.000000027 m 0.000000027 y component of the position vector q Give your answer up to at least three significance digits. 0.000000033 m 0.000000033 I component of the position vector q2 Give your answer up to at least three significance digits. 0.000000018 m 0.000000018 y component of the position vector q2 Give your answer up to at least three…

Q2) A particle of mass 6.00 x 108 kg and charge of -7.20 mC is travelling due east. It enters a uniform magnetic field of 3.00 T that points downwards. After entering the field, the particle completes one-half of a circle and exist the field travelling due west. How much time does the particle spend travelling in the magnetic field?

1) Describe the two fundamental sources of a magnetic field. Draw an example of two different magnetic dipoles we have used in lab. Include their respective magnetic field lines in your diagrams below.

Q3. The vector potential of a single magnetic dipole ñ is given by: m x î" Ã(r) = [Here, r" = r – P] Show that, for a distribution of magnetic dipoles, the total magnetic vector potential can be written in the following form: Ã(r) = J,(r"), du' + ds' What does J and K, represent?

3) Draw the motion of the particle in the magnetic field as shown in the figure. Bin Bin * x x x * * x x Proton Electron X x x x X x x x + * x x x * x x x * x x x * x x x B; Pin X x x x Neutron x x x x * x x x x x x x

Complete Solutions

5. A proton (m₂ = 1.67 x 10-27 kg; e = 1.60 x 10-19 C) enters a 14 T field in a direction par- allel to the direction of the magnetic field. The proton is moving at 105 m/s. What is the mag- nitude of the force felt on the proton?

Magnetic Forces  Problem 19:   Suppose a 2.25 T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 17 A current. What would the Hall voltage be, in microvolts, if the number density of free electrons in copper is 8.34 × 1028m-3.