The scalar and vector potentials are defined as follows: V(x,y,z,t) = 0 Ã(x, y,²,1) = μ₁4, (ct —x)  What are the electric and magnetic fields? (a) Ẽ = 0 and 5 = — 144Î ——μ‚¾‚¸Â and B =——-44,³ (b) E=4ck (c) E = — -—-14,4¸¢Â and B = 1⁄- 14,4,J (d) Ē = 0 and B = 0

Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N · m² /C¥acuum permitivity, en = 8.854 × 10-12 F/mMagnetic Permeability of vacuum, µo = 12.566370614356 × 10¬7 H/rMagnitude of the Charge of one electron, e = -1.60217662 x 10 1º CMass of one electron, me = 9.10938356 × 10 31 kgUnless specified otherwise, each symbol carries their usual meaning. For example, µCmeans micro coulomh Say you have 3 charges q1 = 24, q2 = 27, q3 = -26cated at (0, 13) (7, – 13)and (6, –20}espectively. Now, say you choose four random points on the xyplane denoted by p1 (0, 7) p2 (15, –16) p3 (-5, – 16ànd p4 (0, 13). Note that, all charges are in nano coulombs. And all coordinates are in centimeters. Given this information, answer the following questions: a)Calculate the relative position vector that points from p4 to q2. x component of the vector Give your answer up to at least three significance digits. m y component of the vector Give your answer up to at least three significance…

y Figure 3: 7= xi+ yj+zk = pcos cos oi + p sin oj + zk = pp+ zk and i = dr dt -p sin oi + p cos oj + k = po + zk . Notice that cyclotron angular velocity we = do COS is a negative constant, i.e. in the figure the particle is circulating clockwise. 3. Consider a charged particle, q, in the presence of a magnetic field B with velocity i = it + üz = ü + ij at position relative to origin experiencing a magnetic force qü x B. From the second law it follows that the kinetic energy of the particle remains constant[ see figure 3] : d mv2 m[v² + v?] du - 0 = dt (a) : qü x B m ä - i [gữ x B] = ū. [m- = constant (True, False) dt 2 (b) : A [B x Č) Č [Ä x B] = B IC x A] (True, False)

Four point charges with charge +q=6.7µC are arranged in a square of side length L = 5.0 cm in the x/y plane. A fifth point charge -q=-6.7µC is placed in the center of the square but displaced a distance d=3.6 cm in the z direction. What is the net force on the negative point charge?