Consider an isosceles triangle of charges.  At (a, 0), there is a 2 nC charge.  At (-a, 0), there is a -5 nC charge.  At (0, b), there is a -1 nC charge.  Here a = 3.7 m and b = 7.7 m.  Calculate the electric potential at the origin, in V.  Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225

Q4 is inde the image:

What is the electric potential in volts (relative to zero at infinity) at the origin for a charge of uniform density 13.97 nC/m is distributed along the z axis from z = 2.1 m to z = 6.45 m.   Round your answer to 2 decimal places.

Problem 2: A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder? a) Compute the surface charge density n of the shell from its total charge and geometrical parameters. Vcenter = 1 Q 2 In 4л€ L t₂ S² b) Which charge dq is enclosed in a thin ring of width dz located at a distance z from the center of the cylinder (shown in Fig.2)? Which potential dV does this ring create at the center (you need to use the formula derived in the textbook for the potential of a charged ring along its axis). dz c) Sum up the contributions from all the rings along the cylinder by integrating dV with respect to z. Show that (The integral that you need to use here is d dt √²+a² R² + 1/2 + 1/1/20 √√R² +4-4 L² R2 L R FIG. 2: The scheme for Problem 2 [2 = ln(t + √₁² + a²) 1².) 2

A point charge of 0.80 uC at the origin. What is the electric potential at the point x=-40 cm?

Problem 3.01. (a) Find the electric field between two plates which are separated along the y-axis Ay = 6.00 mm, where the bottom plate has a potential V₂ = 150. mV and the top plate has a potential V₁ = 5.00 mV. (b) What is the potential at a distance Ay' = 2.00 um from the bottom plate?

The charge density on a disk of radius R = 11.6 cm is given by o = ar, with a = 1.46 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 44.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R A

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)?

Given an electric potential of   find its corresponding electric field vector. Sol. Using the concept of potential gradient, we have   Since we only have, radial direction (r). Then, the del-operator will be   By substitution, we get   Evaluating the differential, we, get the following  *(q/)

4. Figure below shows a ring of outer radius R = 13.0 cm, inner radius r= 0.200R, and uniform surface charge density o = 6.20 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.0OR from the center of the ring. %3D R