There are 3 thin conductive infinitly thin spherical shells with a charge on each shell of +2Q. The innermost shell has a radius of R. Another of the shells has a radius of 2R. The outermost shell has a radius of 3R.  Draw a graph of E vs R. Make sure to show the values of E(3R), E(2R), and E(R).

Two point charges, with charges q and -2q are situated above a grounded conducting plane, as shown. a) What is the dipole moment, p, of this configuration (including any contribution from the grounded conducting plane)? b) What is the surface charge density, o(r), induced on this grounded plane by these charges? -2q d d

Please don't provide handwritten solution .......

Consider a cube of side a with 8 charges (4 with charge +e and 4 with charge -e) at the 8 corners. a Since there are a total of 8 charges, there are 28 pars. This may seem like a lot of terms to add, but many of the terms are identical. For example, 12 of the pairs are of opposite sign and separated by an edge of the cube (a distance a). Also, 12 of the pairs are of the same sign and separated by a diagonal of one face (a distance √2 a). Finally, 4 of the pairs are of opposite sign and separated by a diagonal of the cube (a distance √3 a). Calculate the total electrostatic potential energy of this configuration by summing over all the pairs of charges. Give your answer as the numerical coefficient of the following expression U= 4²4 Give your answer to 4 significant figures, and make sure you include the proper sign.

An infinite sheet lie on the xz plane and z axis points outward from the page (not shown). A solid non-conducting sphere of radius R is placed at h+r distance away from the infinite sheet. Use the following values of these quantities charge density of sphere ρ=44pC/m^3, the charge density of the infinite sheet σ=−20pC/m^2, the radius of the solid sphere R=4.0m, the radius of the Gaussian sphere r=8.0m value of h=2.0m. (here 1pC means pico coulomb charge that is, 10^−12C.) Step 1 Consider the infinite sheet only for this step a) Find the magnitude of the electric field at points P1 and P2 due to infinite sheet only. (Note: the magnitude of a vector is a positive quantity.) b) Find the net flux through the Gaussian sphere of radius r due to infinite sheet only. Step 2 Consider the solid non-conducting sphere only for this step c) Find the net flux through the Gaussian sphere of radius r due to the solid sphere only.

Calculate the total force on a charge of 6.00 µC placed at the center of curvature.

Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. The charges of each marble are q1 = 6.20 µC, q2 = 1.01 µC, and  q3 = −2.14 µC.  Marble q1 is a distance r1 = 3.00 cm to the left of the marble q2, while marble q3 is a distance r3 = 2.00 cm to the right of the marble q2, as shown. Calculate the magnitude of the electric field a distance r' = 1.00 cm to the left of the center marble. What is the electric field due to each individual marble? How do you find the total or "net" electric field when you have several electric fields?  Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of −3.62 µC, calculate magnitude and direction of the force on it.

Three charged particles are at the corners of an equilateral triangle as shown in the figure below. (Let q = 4.00 µC, and L = 0.750 m.) Three charged particles lie in the x y coordinate plane at the vertices of an equilateral triangle with side length L. Positive charge q is at the origin. A charge of 7.00 µC is in the first quadrant, along a line 60.0° counterclockwise from the positive x-axis. A charge of −4.00 µC is at (L, 0). (a) Calculate the electric field at the position of charge q due to the 7.00-µC and −4.00-µC charges.Once you calculate the magnitude of the field contribution from each charge you need to add these as vectors.kN/C î + You have given the magnitude of the field due to the 7.00-µC charge. What is the y component of this field? kN/C ĵ(b) Use your answer to part (a) to determine the force on charge q.mN î + mN ĵ

Consider a thin plastic rod bent into an arc of radius R and angle a. The rod carries a uniformly distributed negative charge -Q. (Note: the diagram may have the incorrect sign.) y α R -Q X What is the x component of the electric field at the origin? (Enter your responses in terms of the symbolic quantities mentioned in the problem. To make things easier, just write the letter "a" for the angle a, and use the Coulomb constant k rather than the unwieldy 1/4no.) Ex = k*Q*sin(a)/(a*R^2) Computer's answer now shown above. Tries 0/6 What is the y component of the electric field at the origin? Ey = k*Q*(1-cos(a))/(a*R^2) Computer's answer now shown above. Tries 0/6 Follow the steps outlined in class and in the textbook: 1. Use a diagram to explain how you'll cut up the charge distribution, and draw the AE contributed by a representative piece of charge at a given location. 2. Express algebraically the contribution each piece makes to each vector component of the electric field. Indicate…