If the electric potential is given by V(x, y) =  (12 V/m2) x2 + (3 V/m) y determine the magnitude of the electric field, in V/m, at the origin

Three charges are placed on a line with q1= 15 mC, q2 = 20 mC and q3 = -70 mC. Here d = 10 cm and h = 7 cm. Find the electric field (magnitude and direction) and the electric potential at the location of the X.

a) Calculate how much work is required to set up the arrangement if the charges are initially infinitely far apart and were at rest. (Hint: Use the relation between work done by external agent and total electric energy of the system) Here a = 20 cm, b= 9 cm and the three charges are gl = 28 µC, q2 = 25 µC q3 = 30 µC b) Calculate the potential at the controid(point p) of the triangle. c) Consider a spherical surface of radius r = 5a centered at p. Find the total electric flux through the surface. Total Electric Flux

Suppose that the electric potential V in a certain region is given by   V=A⁢x2−B⁢x+C   where A=2.35 V/m2, B=4.25 V/m, and C=7.25 V. Find the magnitude of the electric field E at the point ?=1.65 m.

What is the magnitude of an electric field at the point (3.00 i – 2.00 j + 4.00 k) m, if the electric potential is given by ? b V=2xyz^2

A point charge of q = 5.0 × 10−8 C is placed at the center of an uncharged spherical conducting shell of inner radius 6.0 cm and outer radius 9.0 cm. Find the electric potential at (a) r = 4.0 cm, (b) r = 8.0 cm, (c) r = 12.0 cm.

The electric potential at x = 3.00 m is 120 V, and the electric potential at x = 5.00 m is 190 V. What is the x component of the electric field in this region, assuming the field is uniform? (a) 140 N/C (b) 2140 N/C (c) 35.0 N/C (d) 235.0 N/C (e) 75.0 N/C

Which of the following statements is true about the magnitude of the net electric field E and the net electric potential V, at the center of the square as shown below?Which of the following statements is true about the magnitude of the net electric field E and the net electric potential V, at the center of the square as shown below? E = 0; V ≠ 0     E ≠ 0; V = 0     E = 0; V = 0     E ≠ 0; V ≠ 0

(a) The electric potential in a region is given by the equation V(x, y) = (1.00) xyz +2.00v. sin (3.00-x). What is the force on a 65.4 mC located at position (3.30 m, 4.21 m,-1.80 m)? Give your answer in vector component notation. (b) The electric potential in a region is given by the equation V(x, y, z) = (2.40)x²y + (1.5 V)e (1.002). What is the force on a 12.6 mC located at position (-1.30 m, 2.48 m,-2.10 m)? Give your answer in vector component notation.

What is the magnitude of the electric field at the point (8.10i - 5.80j+9.40 k) m if the electric potential is given by V= 8.50xyz?, where Vis in volts and x, y, and z are in meters?