The electric potential is given by the following expression: V(x, y, z) = x²yz + 2y²z, where V is in volts. Determine the electric field (magnitude and direction) at point (1, 1, 2).

In a certain region of space, the electrical potential is given by the relationV(x,y,z) = Axy – Bx2 + Cywhere A, B, and C are positive constants. Calculate the x, y, and z components of the electric field.

Assume that the electric potential field in a certain region is given by phi(x, y, z) = a * (x2 + y2 + z2), where a is a constant. Find the electric field vector E(x, y, z) in this region.

Suppose the electric potential due to a certain charge distribution can be written in Cartesian Coordinates as V(x,y,z)=2 x10 z³ y? . What is the magnitude of the electric field at the point (1,1,1)? Your answer should not include units. And write your answer in 1 decimal places. Maximum of 3% error is accepted in your answer.

... Path of trajectory AV w An electron is fired at a speed v¡ = 3.4 x 106 m/s and at an angle 0; = 30.5° between two parallel conducting plates as shown in the figure. If s = 1.5 mm and the voltage difference between the plates is AV = 98 V, determine how close, w, the electron will get to the %3D %3D 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.

In a certain region of space there is a uniform electric field of magnitude E.  What are the potential difference of: (V2 − V1); (V3 − V1); and (V4 − V1)

What is the potential difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?

The electric potential in a certain region isV = α x^2y^2 + β z^2(x^2 − γ) + δ y^3z ,where α = 8 V/m^4, β = 4.6 V/m^4,  γ =5.1 m^2, and δ = 5.6 V/m^4.What is the y component of the electric field Ey at (5.3 m, −1 m, 6.9 m)?Answer in units of V/m.

A dielectric cylinder with absolute permittivity e, has radius b and height L. The bottom plate of the cylinder is positioned at x-y plane, concentric with the z-axis. The polarization vector in the dielectric cylinder is given P = 6Por cos(o), where Po is a constant. Find (a) Bound charge densities (b) The total charge of the cylinder. (C) Write the integral expression of the potential at P (0,0,0) explicitly. Define the integral limits and all the components in the integrant expression. Do not take the integral.

Problem 2: The electric field in a certain region is given by the equation where a = 11.44 N/(C · m³), b = 8.02 N/C, and n = 5. ▲ Calculate the potential difference, in volts, from point x₁ = 0.63 m to point x2 = 1.68 m, i.e., AV = V (x₂ ) − V (x₁ ) . AV = V cos() asin() tan() π ( ) 7 8 9 acos() E ^^^ 4 5 6 sinh() 1 2 3 tanh() cotanh() E = (ax" - b) i^ sin() cotan() atan() acotan() cosh() O Degrees Radians 1 HOME + 0 END VO BACKSPACE DEL CLEAR