Please work it this problem and use parentheses!!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? Express your answer in terms of Q , L , R and appropriate constants
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Please work it this problem and use parentheses!!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? Express your answer in terms of Q , L , R and appropriate constants
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- Problem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: What is The potential at A:.An insulated solid sphere of radius R has a uniform charge density (row). Compute the electric potential everywhere i.e. inside and outside. Draw a potential vs r graph. [electric potential. not field. please follow instructions]A hollow, thin-walled insulating cylinder of radius R and length L (like the cardboard tube in a roll of toilet paper) has charge Q uniformly distributed over its surface. Part A Calculate the electric potential at any point x along the axis of the tube. Take the origin to be at the center of the tube, and take the potential to be zero at infinity. Express your answer in terms of the given quantities and appropriate constants. Part B Use the result of part A to find the electric field at any point x along the axis of the tube. Express your answer in terms of the given quantities and appropriate constants.
- Please answer fast A long cylindrical pipe of radius R is made of two thin, conducting “half pipes”, separated by a thin insulator. One is held at potential +V0 and the other is held at −V0. For the interior of the pipe, express the potential as a series and provide an integral expression for the coefficients in each series.A thin uniformly charged arc with radius R= 2 cm is shown in the figure below. The total charge of the arc is Q= 81 µC. Point 0 is the origin at the center of the arc. R Calculate the linear charge density 1. Write down an (a) expression for the infinitesimal charge dq. Write down the potential dV at point O due to the infinitesimal charge dq.A conducting solid sphere of radius a, carrying a charge +Q is surrounded by a thin conducting spherical shell (inner radius b) with charge -Q. (a) What is the direction and magnitude of the electric field E in the three regions below. Show how you obtain your expressions.i. r b (b) What is the electric potential V(r) in these same three regions. Take the electric potential to be zero at infinity. (c) What is the electric potential difference between the outer shell and the inner sphere, AV=V(b) -V(a)? (d) What is the capacitance of this spherical capacitor? (e) If a negative charge -3Q is placed anywhere on the inner sphere of radius a, what charge appears on the outside surface of the thin spherical shell of inner radius b? a
- Two equal disks of external radius R and internal radius R / 2 are loaded with positive and uniform charge distributions σ. The discs lie in parallel planes separated by a distance R, but with their centers located on the same axis, as shown in figure 2. Take this axis as Z, and as the origin of coordinates or the midpoint between the rings. 1. Obtain the expression of the electrostatic potential created by these distributions in the points on the Z axis. Where is the potential maximum? 2. Obtain the electric field expression for the points on the Z axis. How does the electric field for z >> R? 3. Determine the work that must be done to bring a point charge q from the infinity to point O. 4. A particle of mass m and charge q> 0 is thrown from infinity through the Z axis. Determine the speed with which the particle must be thrown so that at point O stay at rest.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)?Calculate the potential at the following distances from the point charge q and explain your result. Assume that at infinity the potential is zero hollow conducting sphere of inner radius c=15m and outer radius d=25m what is the Potential at r=c? what is the Potential at r=c+d2?
- Find the force vector F on an object of mass m the uniform gravitational field when it is at height z = 0. The +z direction is up. Express vector force in terms of m, z. g. and k, where k is the unit vector in the +z direction. To create the k character: In the equation editor window, select "More", then select "Vectors", and you will find what you need. To write out a vector: for example, if the answer has both x and y components, you would answer in the format Fi + Fj F(z) = -mgk Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector. Express U(z) in terms of m. z. and g. U(2)= In what direction does the object accelerate when released with initial velocity upward? downward Oupward or downward depending on the initial mass m. upward or downward depending on the initial velocity upward Now consider the analogous case of a particle…A solid insulating sphere of radius a = 4 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly -118 µC/m³. Concentric with charged with a charge density p = the sphere is an uncharged spherical conducting shell of inner radius b = 12.8 cm, and outer radius c = 14.8 ст. P(40)C. A cylindrical surface of radius R and length L is oriented parallel to the z-axis, centred on the origin. The surface charge density ps on the cylindrical surface is constant. Find the electric potential at all points z on the z-axis. Sketch a graph of the result, i.e. V(z). (Hint: see Appendix C.3) 3A