11) A thin rod extends along the -axis from r = -a to x = a . The rod carries a positive charge +Q uniformlydistributed along its length 2a with charge density A, as shown in Figure 7.• a) Use dV =S to show that the electric potential at point P is given byx +aInx - aV(x) =4T€0• b) What is the electric potential of the rod at x = 4a and r = 2a?c) What is the electric potential difference between x = 4a and x =• d) Now consider that there is an electron moving from a = 4a to x = 2a. What is the change in theelectrostatic potential energy (AU) of the electron? (calculate it in terms of the parameters defined in theproblem}e) Explain the reason why AU in part d is positive or negative.dx'aFigure 7: A thin rod of uniform charge density A used in question 11

Disclaimer: “Since you have asked posted a question with multiple sub-parts, we will solve the first…

Answered: 11) A thin rod extends along the x-axis…

Similar questions

A) find the total electric potential difference due to these charges at point P located at (3,4) m coordinates. B)How much work required to bring a third point charge of 4micro coloumb from infinity to p?
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 =
A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly distributed along its length 2a with charge density λ, as shown in Figure attached. a) Use dV = 1/4πε0 ∫ dq/r to show that the electric potential at point P is given by: V(x) = (λ/4πε0) ln(x + a/x − a) b) What is the electric potential of the rod at x = 4a and x = 2a? c) What is the electric potential difference between x = 4a and x = 2a?
If the electric potential is zero at infinity, is the electric potential at the surface of a conductor with a total charge Q where Q < 0 positive or negative?
3) A charged wire is in the shape of half a circle with radius R. The charge density on the wire is given by λ(0) = 2 sin 0, as shown in the figure. R 0 2 (0) = 20 sin 0 X (a) Find the electric potential V(x) for points along the x-axis, for x > 0. (b) Graph V(x) from x = 0 to x = 3R.
For a sphere of radius R = 12.1 m that is charged with a non-uniform volume charge density: b p(r) = as =ar + with a = figure). 6.8 x 10-12 C/m² and b = 6.6 × 10-12 C/m² and r is the distance from the center of the sphere (see R Calculate the electric potential at distance r = 8.5 m from the center. Assume that the potential on the surface of the sphere equals to zero, that is (R) = 0. 21.0 x
13) Consider the following potential between two atoms, given as a function of the center-to- center separation between the atoms. PE[in units of 10-²1 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 6 r[in units of 10-10 m] A: 1.12 x 10-10 m B: 4.0 x 10-10 m C: 2.25 x 10-10 m D: 3.0 x 10-10 m E: 2.5 x 10-10 m 8 If this system of two atoms has a total energy of Etotal = -0.5×10-21 J, what is the maximum separation these two particles can reach?
Electric Potential of Distributed Charge 4. An evenly charged wire of length L has a total charge of Q distributed on it and is located on the x-axis a distance a away from the origin as drawn. Set up the integral that could be solved to determine the electric potential at any point on the y-axis, (0,yo). You do not have to evaluate the integral.
O:11)