General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 1 Review (Electrostatic)

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 2 [1] Three charges are located in the XY plane as Shown in the figure. Q 1 = - 3 nC, Q 2 = 5 nC Q 3 = 3 nC. The distance between Q 1 and Q 2 is 8 m and between Q 2 and Q 3 is 6 m. Find: a)The electric field due to the charges at the origin O. b)The electric potential due to these charges at the origin O. c) What is the direction of the net force on the point O.

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 3 a)The electric field due to the charges at the origin O.

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 4 b) The electric potential due to these charges at the origin O. c) What is the direction of the net force on the point O.

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 5 [2] Two point charges are located on the x-axis as follows: charge Q1 = 8x10 -9 C is at x = 0 and charge Q 2 = -1x10 -9 C is at x = 1cm. What is the net force in the x direction on a third charge,Q 3 = +2x10 -9 C, placed at x = 2 cm ?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 6 [ 3] In a hydrogen atom an electron circles a proton. Since the mass of the proton is much greater than the mass an electron, assume that the proton stays fixed in space and the electron rotates around it with radius 0.529x m. What is the velocity of the electron?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 7 [ 4] A uniform electric field exists in the region between two oppositely charged plane parallel plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate 2x10 -8 s later. If the magnitude of the electric field is 4x10 3 N/C, what is the separation between the plates?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 8 [5] Two charged particles are placed on the x-axis as follows: Q 1 = 1x10 -9 C at x = 0 m and Q 2 = -2x10 -9 C at x = 1.6 m. Where on the x-axis is the electric field zero? The electric field can only be zero where the field due to Q 1 and Q 2 point in opposite direction. This occurs both for x 1.6 m, however since Q 2 is greater in magnitude, one must be further away from it in order to have the magnitudes of the fields due to Q 1 and Q 2 be equal. This means the field is zero in the region x<0. Sitting the magnitude equal,

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 9 [6] Two stationary point charges are arranged on the x-axis as follows: Q 1 = 2.4x C at x = 0 m and Q 2 = -1.2x C at x = 1 m. An electron is placed at x = 2 m and let go. What is the velocity of the electron when it reaches x = 3 m. This is a conservation of energy problem. The initial kinetic energy of the electron is zero. The initial and final potential energy of the electron are: Consequently, the final kinetic energy is And the final velocity of the electron is

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 10 [7] Using the superposition principle determine the electric field at point P in Fig. Using the convention that a positive electric field is up and a negative electric field is down, the net electric field at p is

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 11 [8] A 1 Coulomb charge is located at the origin. Another charge, Q, is located at x = 3 m. If the electric field is zero at x = 1 m, what is Q? The electric field due to the 1C charge is in positive x-direction at x=1m. In order to cancel this field, the charge at x=3m must be positive so that its electric field is in the negative x-direction at x=1m. The two field will cancel if they have the same magnitude.

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 12 V C1C1 C2C C3C3 C 1 = 10  F C 2 = 5.0  F C 3 = 4.0  F [9] a) Find the equivalent capacitance of the entire combination. C 1 and C 2 are in series. C 12 and C 3 are in parallel.

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 13 b) If V = 100 volts, what is the charge Q 3 on C 3 ? C = Q/V c) What is the total energy stored in the circuit?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 14 [10] A wire of uniform charge density and length L lies along the x axis as shown in Figure. What is the electric potential at point A?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 15 [11] Determine the point nearest the charges where the total electric field is zero. Take the µC charge to be at the origin of the x axis  C-2.50  C 1.00 m 0.39 m [12] The plates of a parallel plate capacitor are separated by 1 x 10 –4 m. If the material in between them is a jelly with a dielectric constant of 2.26, what is the plate area needed to provide a capacitance of 1.50 pF? 7.50 x 10-6 m2

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 16 [13] Find the charge on the 2  F capacitor in the following circuit. [14] Each of the protons in a particle beam has a kinetic energy of 3.25x J What are the magnitude and direction of the electric field that will stop these protons in a distance of 1.25 m? 1.63 x 104 N/C and opposite to the motion 2  F 4  F 2  F 12 V 18µC

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 17 [15] Three point charges are fixed on the corners of an equilateral triangle whose one side is b as shown in Figure. 1. What is the magnitude of the Coulomb force acting on charge –q due to presence of other charges? 2. What is the value of the electric potential at the center (point A) of positive charges? 3. What is the electric potential energy of system?

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 18 [16] The stored energy of a capacitor is 3.0 J after having been charged by a 1.5 V battery. What is the energy of the capacitor after it is charged by 3.0 V battery? [17] Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure. 7µF and 5µF series 4µF, 6µF and 2.9µF parallel

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 19 [18] Two capacitors when connected in parallel give an equivalent capacitance of 9.00 pF and give an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor? in parallel in series Solve eq.1&2