In a given region of space the electric potential has the following form: V(r, y, 2) = 3r°y + 92 – 10y²24 a) Determine the appropriate units for the constants in front of each term. b) Determine the É in this region of space. c) Calculate the value of the potential and the E at (4,-5,3) m.

Immediately outside a conducting sphere of unknown charge Q and radius R the electric potential is 240 V, and 10.0 cm further from the sphere, the potential is 140 V. (a) Determine the radius R of the sphere (in cm).   cm (b) Determine the charge Q on the sphere (in nC).   nC (c) The electric potential immediately outside another charged conducting sphere is 260 V, and 10.0 cm farther from the center the magnitude of the electric field is 380 V/m. Determine the radius (in cm) of any sphere for which this is possible. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.) R1= cmR2= cm (d) Determine the charge on the sphere (in nC) for each value of R. (If only one value exists, enter "NONE" in the second answer blank.) q1= nCq2= nC

A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity.  V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =

(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.

Three-point charges: Q = - 2 µC, Q, = 4 µC, and Q = – 2 µC 4 иС, апd Q, positioned in the A, B, and C corners of a square with length of 0.41m. Find: are (a) The electric intensity created by the Q, Q, and Qz in the fourth square corner D. 3. (b) The electric potential in point D (c) The work needed to move a point-charge Q = 1 °C from corner D to the center of the square.

In a certain region of space, the electric potential is V(z,9,2) = Czy – Ar + By %3D where A, B and C are positive constants. Calculate the r, y and z components of the electric fiekd.

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.

It is known that the electric quantity Q is uniformly distributed on the spherical surface of radius R, that is, the electric charge per unit area isQ/4piR^2Find the electric potential distribution generated by this charged sphere in space.

What is the potential (in V) 0.530 ✕ 10−10 m from a proton (the average distance between the proton and electron in a hydrogen atom)?

The electric potential on the surface of a charged conducting sphere is 210 V, and 10.0 cm farther from the center of the sphere the potential is 140 V. (a) Determine the radius of the sphere. HINT: Use a ratio of the two given potentials to solve for the radius. 20 cm (b) Determine the charge on the sphere. 4.67 nC The electric potential on the surface of another charged conducting sphere is 240 V, and 10.0 cm farther from the center the magnitude of the electric field is 410 V/m. (c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.) HINT: Use the ratio of the potential at the surface to the E field at the surface plus 10.0 cm to solve for the radii. cm r2 = cm (d) Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.) 91 = nC 92 =