Álong the x-axis, the potential is given by: V(x) = 2.16 - 0.251x - 0.137x where x is in meters, and V is in Volts. Find the acceleration if a proton as it passes through the point (0.316 m, 0), in m/s“. The sign of the answer will give the direction of the force.

Over a certain region of space, the electric potential is V = 4x – 1x2y + 2yz2. (a) Find the expressions for the x, y, z components of the electric field over this region. (Use any variable or symbol stated above as necessary.) Ex Ey Ez %3D (b) What is the magnitude of the field at the point P that has coordinates (1.00, 0, -8.00) m? N/C

A long coaxial cable carries a positive uniform volume charge density, ρ, on theinner cylinder (radius a), and a negative uniform surface charge density, σ, of thecylindrical shell (radius b). The surface charge has a magnitude so that the cable asa whole is electrically neutral.                                                                                                                                                                                                    find the electric potential V atthe center of the coaxial cable, using s = infinity as a reference point

The three charges in the figure below are at the vertices of an isosceles triangle. Let q = 3.50 nC and calculate the electric potential in KV at the midpoint of the base. (Let d1 = 1.00 cm and d2 = 7.00 cm.)

A region of space contains an electric potential given by V(x,y,z) = 4x2y – 2z + 5x3yz2. Determine the componentsand the magnitude of the electric field at the point (1, 5, 0).

The clectric potential in a region of space is V (x, y) 200 Volts, where x and x²+y² y are in meters. What are the strength and direction of the clectric ficld at (x, y) = (2.0 m, 2.0 m)? Give the direction as an angle cw or ccw (specify which) from the positive r-axis.

(a) What is the magnitude of the electric field in a region where the potential is given by the expression V = ax2 + b where a = −600 V/m2 and b = 195 V? (Substitute numerical values, and express your answer in terms of x. Assume SI units, but do not include units in your answer.) E =  V/m2   (b) What is the magnitude of the electric field at x = 6.25 m?  V/m

(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?

Sketch the electric field lines of the parallel plate capacitor and the variation of the following parameters as a function of position x inside the capacitor: electric potential produced by the capacitor, potential energy of the proton, total energy of the proton, and kinetic energy of the proton.