General Physics II, Lec 3, By/ T.A. Eleyan 1 Lecture 3 The Electric Field

General Physics II, Lec 3, By/ T.A. Eleyan 2 Electric Field Suggests the notion of electrical field (first introduced by Michael Faraday ( ). An electric field is said to exist in a region of space surrounding a charged object. If another charged object enters a region where an electrical field is present, it will be subject to an electrical force.

General Physics II, Lec 3, By/ T.A. Eleyan 3 Consider a small charge q 0 near a larger charge Q. We define the electric field E at the location of the small test charge as a ratio of the electric force F acting on it and the test charge q 0 This is the field produced by the charge Q, not by the charge q 0 Electric Field & Electric Force

General Physics II, Lec 3, By/ T.A. Eleyan 4 Electric Field Direction The direction of E at a point is the direction of the electric force that would be exerted on a small positive test charge placed at that point E E

General Physics II, Lec 3, By/ T.A. Eleyan 5 Electric Field from a Point Charge Suppose we have two charges, q and q 0, separated by a distance r. The electric force between the two charges is We can consider q 0 to be a test charge, and determine the electric field from charge q as

General Physics II, Lec 3, By/ T.A. Eleyan 6 + r q qoqo E - r q qoqo E If q is +ve, field at a given point is radially outward from q. If q is -ve, field at a given point is radially inward from q.

General Physics II, Lec 3, By/ T.A. Eleyan 7 Electric Field Lines To visualize electric field patterns, one can draw lines pointing in the direction of the electric field vector at any point. These lines are called electric field lines.lines 1.The electric field vector is tangent to the electric field lines at each point. 2.The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region. 3.No two field lines can cross each other. Why?cross

General Physics II, Lec 3, By/ T.A. Eleyan 8 The electric field lines for a point charge. (a) For a positive point charge, the lines are directed radially outward. (b) For a negative point charge, the lines are directed radially inward. Note that the figures show only those field lines that lie in the plane of the page.

General Physics II, Lec 3, By/ T.A. Eleyan 9 The electric field lines for two positive point charges. The electric field lines for two point charges of equal magnitude and opposite sign (an electric dipole)

General Physics II, Lec 3, By/ T.A. Eleyan 10 Question : Two charges q 1 and q 2, fixed along the x-axis as shown, produce an electric field E at the point (x,y)=(0,d), which is the directed along the negative y-axis. Which of the following is true? 1.Both charges are positive 2.Both charges are negative 3.The charges have opposite signs

General Physics II, Lec 3, By/ T.A. Eleyan 11 A system of two oppositely charged point particles is called an electric dipole. The vector sum of the electric field from the two charges gives the electric field of the dipole (superposition principle). We have shown the electric field lines from a dipole Electric Field from an Electric Dipole

General Physics II, Lec 3, By/ T.A. Eleyan 12 Example:Example: Two charges on the x-axis a distance d apart  Put -q at x = -d/2  Put +q at x = +d/2 Calculate the electric field at a point P a distance x from the origin

General Physics II, Lec 3, By/ T.A. Eleyan 13 Principle of superposition:The electric field at any point x is the sum of the electric fields from +q and -q Replacing r + and r - we get This equation gives the electric field everywhere on the x-axis (except for x =  d/2)

General Physics II, Lec 3, By/ T.A. Eleyan 14 Problem: (a) Find the electric field at point P in Fig. below. (b) Repeat for q 2 = +1 nC.

General Physics II, Lec 3, By/ T.A. Eleyan 15 Example: Electric Field Due to Two Point Charges Charge q 1 =7.00  C is at the origin, and charge q 2 =  C is on the x axis, m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m. x y m q1q1 q2q m P E1E1 E2E2 E

General Physics II, Lec 3, By/ T.A. Eleyan 16

General Physics II, Lec 3, By/ T.A. Eleyan 17 Problem : Electric Field Due to Four Point Charges Four charges q 1 =10 nC, q 2 =-20 nC, q 3 =20 nC and q 4 =10 nC form a square of edge length 5 cm. What electric field do the particles produce at the square center?

General Physics II, Lec 3, By/ T.A. Eleyan 18 Example In Figure, determine the point (other than infinity) at which the total electric field is zero. Solution: The sum of two vectors can be zero only if the two vectors have the same magnitude and opposite directions.

General Physics II, Lec 3, By/ T.A. Eleyan 19 Problem Three point charges are arranged as shown in Figure (a) Find the vector electric field that the 6.00 nc and –3.00 nc charges together create at the origin. (b) (b) Find the vector force on the 5.00 nc charge.

General Physics II, Lec 3, By/ T.A. Eleyan 20 Motion of charge particles in a uniform electric field An electron moving horizontally passes between two horizontal planes, the upper plane charged negatively, and the lower positively. A uniform, upward-directed electric field exists in this region. This field exerts a force on the electron. Describe the motion of the electron in this region. - veve

General Physics II, Lec 3, By/ T.A. Eleyan 21 Horizontally:  No electric field  No force  No acceleration  Constant horizontal velocity Vertically:  Constant electric field  Constant force  Constant acceleration  Vertical velocity increase linearly with time.

General Physics II, Lec 3, By/ T.A. Eleyan Conclusions: The charge will follow a parabolic path downward. Motion similar to motion under gravitational field only except the downward acceleration is now larger.

General Physics II, Lec 3, By/ T.A. Eleyan 23 -e -Q +Q -Q Phosphor Screen This device is known as a cathode ray tube (CRT)

General Physics II, Lec 3, By/ T.A. Eleyan 24 Continuous Charge Distributions Discrete charges Continuous charge distribution Single chargeSingle piece of a charge distribution +Q 3 +Q 2 +Q

General Physics II, Lec 3, By/ T.A. Eleyan 25 Line charge Cartesian Polar Surface charge Volume charge

General Physics II, Lec 3, By/ T.A. Eleyan 26 A rod of length l has a uniform positive charge per unit length λ and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end. Example: Electric Field Due to a Charged Rod

General Physics II, Lec 3, By/ T.A. Eleyan 27 Example – Infinitely Long Line of Charge y-components cancel by symmetry

General Physics II, Lec 3, By/ T.A. Eleyan 28 Example – Charged Ring perpendicular-components cancel by symmetry

General Physics II, Lec 3, By/ T.A. Eleyan 29 When: The charged ring must look like a point source. 0

General Physics II, Lec 3, By/ T.A. Eleyan 30 Example – Uniformly Charged Disk

General Physics II, Lec 3, By/ T.A. Eleyan 31 Two Important Limiting Cases Large Charged Plate: Very Far From the Charged Plate:

General Physics II, Lec 3, By/ T.A. Eleyan 32 Lecture 4 Discussion

General Physics II, Lec 3, By/ T.A. Eleyan 33 [1] In figure, two equal positive charges q=2x10 -6 C interact with a third charge Q=4x10 -6 C. Find the magnitude and direction of the resultant force on Q.

General Physics II, Lec 3, By/ T.A. Eleyan 34 [2] A charge Q is fixed at each of two opposite corners of a square as shown in figure. A charge q is placed at each of the other two corners. If the resultant electrical force on Q is Zero, how are Q and q related.

General Physics II, Lec 3, By/ T.A. Eleyan 35 [3] Two fixed charges, 1µC and -3µC are separated by 10cm as shown in figure (a) where may a third charge be located so that no force acts on it? (b) is the equilibrium stable or unstable for the third charge?

General Physics II, Lec 3, By/ T.A. Eleyan 36

General Physics II, Lec 3, By/ T.A. Eleyan 37 [4] Find the electric field at point p in figure due to the charges shown. Solution:

General Physics II, Lec 3, By/ T.A. Eleyan 38 [5] A charged cord ball of mass 1g is suspended on a light string in the presence of a uniform electric field as in figure. When E=(3i+5j) *10 5 N/C, the ball is in equilibrium at Θ=37 o. Find (a) the charge on the ball and (b) the tension in the string. Substitute T from equation (1) into equation (2) Substitute by q into equation (1) to find T=5.44*10 -3 N

General Physics II, Lec 3, By/ T.A. Eleyan 39 [6] A 1.3µC charge is located on the x-axis at x=-0.5m, 3.2µC charge is located on the x-axis at x=1.5m, and 2.5µC charge is located at the origin. Find the net force on the 2.5µC charge

General Physics II, Lec 3, By/ T.A. Eleyan 40 [7] Two free point charges +q and +4q are a distance 1cm apart. A third charge is so placed that the entire system is in equilibrium. Find the location, magnitude and sign of the third charge. Is the equilibrium stable?

General Physics II, Lec 3, By/ T.A. Eleyan 41 [8] Two protons in a molecule are separated by a distance of 3.8* m. Find the electrostatic force exerted by one proton on the other. [9] The electric force on a point charge of 4.0mC at some point is 6.9* N in the positive x direction. What is the value of the electric field at that point?

General Physics II, Lec 3, By/ T.A. Eleyan 42 [10] Two point charges are a distance d apart. Find E points to the left P. Assume q1=+1.0*10 -6 C, q2=+3.0*10 -6 C, and d=10cm

General Physics II, Lec 3, By/ T.A. Eleyan 43 [11] Calculate E (direction and magnitude) at point P in Figure.

General Physics II, Lec 3, By/ T.A. Eleyan 44 [12] A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 2.0cm away, in a time 1.5*10 -8 s. (a) What is the speed of the electron as it strikes the second plate? (b) What is the magnitude of the electric field.

General Physics II, Lec 3, By/ T.A. Eleyan 45 [13] Three charges are placed on corners of an equilateral triangle as shown in Figure 1. An electron is placed at the center of the triangle. What is the magnitude of the net force on the electron?

General Physics II, Lec 3, By/ T.A. Eleyan 46 [14] 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?