What is the electric potential at the surface of the cylindrical shell? (r = R) Express your answer in terms of variables Q, L, r, and R. Combine all numerical values together into one multiplier.
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- A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z-axis, and the cylinder is centered at the origin, as shown in (Figure 1). What is the potential V0 in the limit as h goes to zero? Express your answer in terms of q, r, and ϵ0. V attached in image 2.need the last 3 parts of this pleaseplease answer G and H. previous questions are above to help:)
- An electric potential function is given by V(x, y) = 3xy^2 - 2x^2 y - 2 where MKS units are used. Show all work neatly. Don't forget to include units in your answers. Use the back if more room is needed, but note accordingly. What is the electric field vector, E(x, y), in rectangular coordinates? What is the magnitude and direction of the electric field at the point (x,y) = (2,3)? What is the divergence of the electric field at the point (x,y) = (2,3)? What is the curl of the electric field at the point (x,y) = (2,3)?A sphere has radius R and uniform charge density ρ. Take your reference point at infinity and find the potential at all points in space, inside and outside the sphere, then draw your results.e conducting cylinder along the z-axis of radius R is placed in a uniform electric field Ë = E,£. Find the electrostatic potential everywhere. Find the induced surface charge density on the conducting cylinder.
- Point Charge Electric Potentials and Fields 1. An uneven dipole centered on the origin as drawn. The (0,y) separation between the charges is d. The leftmost charge (+3q) is positive and three times as large as the rightmost charge (-q), which is negative. Express all answers in terms of the constants k, q, and d. а. Find the y-component of the electric field as a function of y at the location (0,y). b. Find an algebraic expression for the electric potential at location (0,y). This is the electric potential (voltage) as a function of y, V(y), anywhere the y- axis. dV c. Show that your electric potential satisfies: E, dy d. Why can't we find the other electric field component using our electric ptential dV function and E ? What information are we missing? dx) Consider an infinitely long cylinder with radius R and uniform surface charge density o. a. Find the magnitude of the electric field at a distance s from the axis of the cylinder for s R. c. Using your answer to part b, find the potential difference between two points: s= a and s = b. thor axis with itsplease write in a readable way.
- for y d €0 result, use this potential next. aV i+ i+ k) for y < 0, 0 < y < d 6. (a) Now compute -VV and d < y. - (b) Should your result agree with the electric field E that you calculated in problem 2? Does it agree? 7. What is the value of the integral f E· dr over a closed path? You need to be special clear and compelling here to arn the points. 8. (a) Describe the equipotential surfaces with V = –5,000 Volts. Where are they located? (b) Is there an equipotential volume? If the answer is "yes," describe it. (c) Describe all the equipotential surfaces V = V, for Vo < 0 fixed but arbitrary. Where are they located as a function of Vo?function. 2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: Ao A(z) = { db e exp(-2/a) z≥0 x 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming Þ(r → ∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.B5