Verify that each of the following force fields is conservative. Then find, for each, a scalar potential such that F = -V. F = (3x²yz - 3y)i + (x³z − 3x)j + (x³y + 2z)k.
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- A thin rod has uniform charge per length 3w over its length H. The distance between point A and point B is 3H and the distance between point A and point P is 2H. We introduce an integration variables with 5 = 0 chosen to be at point A and the +s direction to be down. The small red segment has length ds and charge dg. We want to find the electric potential at point P. Draw it out--label the all the lengths and the integration variable! A. dV= B. dV C. dV = D. dV= A Which expression below gives the voltage d'V from the small charge dg in the small segment ds? Choose from the choices (A thru F) below: E. dV= F. dV= B с Kdq √√²+4H² Kdg (s² +4H²) Kdq 5 Kdq √(8+3H)² +4H² Kdg ((s+3H)² +4H²) 3.Kdq H ((8+6H)² +97²)³/2 -P +y >+x What are the limits of integration s? [Select] [Select]3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,A cylindrical shell of radius R, and height his charged with charge that is uniformly distributed over it surface. To find the electric potential due to this shell at point Pa distance d from its right base we take, as an element, a thin ring that has a charge element: ut of dx Select one: O dq = o(2 TRdx) O dq = o(2 Trdr) O dq = p(TR?dx) dq = o(TR?dx) Two concentric conducting spherical shells of radii a and bare charged to a total charge Q. If the two shells are connected as shown. Which of the following is false? en 5 ete D out of REDMI NOTE 9 144 AI QUAD CAMERA
- Consider a particle of mass m acted upon by a central potential (r is distance and a>0 is a constant): U (r) p2 a) What are the constants of the motion? b) Is a circular orbit possible in this potential? If so, state the conditions for it. c) Under what conditions will the particle fall to the center of the potential (r = 0)?Two large charged plates of charge density ±18µC/m² face each other at a separation of 7 mm. Choose coordinate axes so that both plates are parallel to the xy plane, with the negatively charged plate located at z = 0 and the positively charged plate at z = +7 mm. Define potential so that potential at z = 0 is zero (V(z = 0) = 0). Hint a. Find the electric potential at following values of z: o potential at z = -7 mm: V(z = -7 mm) = o potential at z = +1 mm: V(z = +1 mm): = o potential at z = +7 mm: V(z = +7 mm) = = o potential at z = +9.2 mm: V(z = +9.2 mm) = V. V. V. V. b. An electron is released from rest at the negative plate. With what speed will it strike the positive plate? The electron will strike the positive plate with speed of m/s. (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2, enter "3.14E12".)d and e