An electric field is given as E = –10e³(sin2zdx + xsin2zāy + 2xcos2zā,)V/m a. Find Ē at P(5,0,–). b. How much work is done in moving a charge of 2nC an incremental distance of 1 mm from P in the direction of ā¿? äy? ã¸? ãz+ây +ã,?

2. a. Draw a force vector at A for a positive test charge. b. Draw a force vector at point B for a negative test charge. c. How much work is done by the field if a charge of q = 2x 10-3 C. is moved from A to C? d. How much work is done by the field if the same test charge moves from A to D? C A 6V OV 5V 4V 3V 2V 1V

An electron is fired at a speed vi = 4.3 × 106 m/s and at an angle θi = 39.7° between two parallel conducting plates as shown in the figure. If s = 1.7 mm and the voltage difference between the plates is ΔV = 99.8 V, determine how close, w, the electron will get to the bottom plate. Put your answer in meters and include at 6 decimal places in your answer. Do not include units. The x-axis of the coordinate system is in the middle of the parallel plate capacitor.   Round your answer to 6 decimal places.

1. Let E = 400ảy – 300đy + 500ả, in the neighborhood of point P(6,2,-3). Find the incremental work done in moving a 5C charge a distance of 1mm in the direction specified by: a. dx + ảy + đ, b. — 2ӑx + Зау — ӑ, 2. If E = -xảx + yã, V/m, find the work involved in moving a unit positive charge on a circular arc, the circle at the origin, from x = a to x = y = a/V2. 3. Let V = 6xy²z3 + 5 In(x2 + y2 + 3z2)V in free space. Evaluate each of the following quantities at P(2,3, -1), find: а. V b. Е c. |JE|| d. D e. ||D|| f. ån