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- How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?arrow_forwardAn electric potential exists in a region of space such that V = 8x4 2y2 + 9z3 and V is in units of volts, when x, y, and z are in meters. a. Find an expression for the electric field as a function of position. b. What is the electric field at (2.0 m, 4.5 m, 2.0 m)?arrow_forward(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.46 if C1 = 5.00 F, C2 = 10.00 F, and C3 = 2.00 F. (b) If the potential between points a and b is 60.0 V, what charge is stored on C5? Figure P16.46arrow_forward
- If the electric field in the region is given as E = 4 (z ax – y ay + x az) V/m. Determine the potential at point A(-1, 3, 7) m, in volts, if the potential at point B(3, 7, 8) m is 77 volts.arrow_forwardA B 2R 3R 4R Consider an infinitely long nonconducting cylindirical shell of inner radius R and outer radius 2R as shown in the figure. The volume charge density of the cylinder Shell is p = 3r, where r is the distance from the axis of the eylinder. Find the potential difference (AVAB = V- VA) between points A and B at distances 3R and 4R from the axis respecti vely. (Note: R=10cm, = 3 and &, = 9. 10 "E) -12 a) - 2,24x10 V by 2,24x10 V 4,3 x101°V di 4,3x10 V 1,57x 10 Varrow_forwardA dielectric cylinder with absolute permittivity ɛ, has radius b and height L. The bottom plate of the cylinder is positioned at x-y plane, concentric with the z-axis. The polarization vector in the dielectric cylinder is given = r Por, where Po is a constant. Find (a) Bound charge densities (b) The total charge of the cylinder. (c) Write the integral expression of the potential at P (0,0,L) explicitly. Define the integral limits and all the components in the integrant expression. Do not take the integral.arrow_forward
- A thin-walled, hollow, conducting cylinder with radius rbrb is concentric with a solid conducting cylinder with radius ra<rb. Each has length L. The two cylinders are attached by conducting wires to the terminals of a battery that supplies potential V. A solid cylindrical shell, with inner radius rara and outer radius R<rb made of a material with dielectric constant K, slides between the conducting cylinders Determine the capacitance as a function of xx.arrow_forwardConsider a solid cylindrical conductor of inner conductor radius 59 cm and outer conductor radius 97 cm with charge Q that is coaxial with a cylindrical shell of negligible thickness. Find the capacitance, in nF, of this cylindrical capacitor if its length is 86 m and the insulator used is mica (εr = 6).arrow_forwardCompute for the potential difference, in volts, in moving a charge from A(0, 0, 2) m to B(0, 0, 8) m against the electric field due to a ring charge of radius 6 m on the plane z = 0 centered at the origin. The ring has a total charge of 9 nC.arrow_forward
- Five sides of a hollow metallic cube are grounded and the sixth side is insulated from the rest and is held at a potential p (see figure). [TIFR 2012] The potential at the center O of the cube is (a) 0 (b) Ф/6 (с) Ф/5 (d) 2 /3arrow_forwardA uniform insulating sphere of radius a with charge Q1 = 0.8 nCis concentric with a = 11.0 cm conducting spherical shell ofinner radius b = 20.0 cm, outer radius c = 30.0 cm andcharge Q2 = 2.0 nC as shown in the figure.If the center of the sphere is chosen as the origin of thecoordinate system, find the potential differenceV (x = a/2 , y = 0 , z = 0) − V (x = 0 , y = (b + c)/2 , z = 0)in units of Volts.Take 14πε0= 9.0 × 109 Nm2/C2.arrow_forwardProblem 6: Consider two concentric cylinders each of length L. The radius of the inner cylinder is a while the radius of the outer cylinder is b. The medium between the two cylinders is filled with insulating material of permittivity ɛ. Determine the capacitance of the structure formed by the two ylinders per unit length. Consider L much greater than the cylinders' radii.arrow_forward
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