Tow concentric spherical shells, of radii a = 3 m and b = 12 m. The inner one carries a charge %3D %3D 2 TEO, and the outer on a charge -2 TE0 (both of them uniformly distributed over the surface). The energy of this configuration is:
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- A 10cm10cm piece of aluminum foil of 0.1 mm thickness has a charge of that spreads on both wide side surfaces evenly. You may ignore the charges on the thin sides of the edges. (a) Find the charge density. (b) Find the electric field 1 cm from the center, assuring approximate planar symmetry.A charge of 30C is distributed uniformly a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.An aluminum spherical ball of radius 4 cm is charged with 5C of charge. A copper spherical shell of inner radius 6 cm and outer radius 8 cm surrounds it. A total charge of 8C is put on the copper shell. (a) Find the electric field at all points in space, including points inside the aluminum and copper shell when copper shell and aluminum sphere are concentric. (b) Find the electric field at all points in space, including points inside the aluminum and copper shell when the centers of copper shell and aluminum sphere are 1 cm apart.
- Two 10cm10cm pieces of aluminum foil of thickness 0.1 mm face each other with a separation of 5 mm. One of the foils has a of +30C and the has 30C . (a) Find the charge density at all surfaces, i.e., on those facing each other and those facing away. (b) Find the electric field between the plates near the center assuming planar symmetry.A long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically a charged long aluminum rod of radius 1 cm with a charge density of 4 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the copper shell has exactly charge to that of the aluminum rod while the outer surface of the copper shell has the same charge as the aluminum rod. Find the magnitude and direction of the electric field at points that are at the following distances from the center of the aluminum rod: (a) 0.5 cm, (b) 1.5 cm, (c) 2.5 cm, (d) 3.5 cm, and (e) 7 cm.A non-conducting spherical shell of inner radius a1 and outer radius b1 is uniformly charged with charged density p1 inside another non-conducting spherical shell of inner radius a2 and outer radius b2 that is also uniformly charged with charge density p2 . See below. Find the electric field at space point P at a distance r from the common center such that (a) rb2 (b) a2rb2 , (c) b1ra2 , (d) a1rb1 , and (e) ra1 .
- An infinite sheet of charge with surface charge density o = -87 C/m? lives in the x-y plane. A thin rod of charge with length L = 13.0 cm is placed along the +z-axis that the end closest to the sheet is located a distance d = 2.0cm away from the sheet. When held at this position, the linear charge density of the rod can be described by K =az, where a = +35 nC/m. 1, What is the force F on the rod from the sheet? 2, Can you draw a picture to represent it?) Two concentric spherical shells of radii r and 2r are connected by a wire, as shown. If the system is charged to a total charge Q, the electric charge on the outer shell is:What is the flux through the total surface of a cube of side length 20.0 cm centered on a point charg of -4.00nc? A metal sphere carrying net charge +6.00 uC is placed around -4.00 uC charge. What is the charges on the interior and exterior surfaces of the metal sphere? Justify your answer.
- Two infinite line charges with uniform linear charge densities λ1 >0 and λ2 < 0, are oriented parallel to the z-axis; see figure below. Thefirst line charge intersects the x-axis at x = −3a while the other one atx = 9b, where a and b are both positive constants (in units of m). Whatis the net electric field at the origin due to these line charges?A conducting sphere of radiusais placed at the origin surrounded by a spherical conductingshell of inner radiusband outer radiusc. The sphere carries a charge of−3Qwhile the outershell is charged to 2Q. Use Gauss Law to find E of the following: c) inside the shell (b < r < c) d) outside the shell (r > c)The figure shows two concentric rings, of radii R and R' = 2.54R, that lie on the same plane. Point P lies on the central zaxis, at distance D = 4.17R from the center of the rings. The smaller ring has uniformly distributed charge Q = 5.71 × 10-6 C. What is the uniformly distributed charge on the larger ring if the net electric field at P is zero?