Ch 22: Electric Force & Field; Gauss' LawWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Intro to Electric Fields

Practice: A 1.5uC charge, with a mass of 50g, is in the presence of an electric field that perfectly balances its gravity. What magnitude does the electric field need to be, and in what direction does it need to point?

Concept #2: Electric Field due to a Point Charge

Example #1: Zero Electric Field due to Two Charges

Practice: If two equal charges are separated by some distance, they form an electric dipole. Find the electric field at the center of an electric dipole, given by the point P in the following figure, formed by a 1C and a – 1C charge separated by 1 cm.

Example #2: Electric Field Above Two Charges (Triangle)

Practice: 4 charges are arranged as shown in the following figure. Find the electric field at the center of the arrangement, indicated by the point P.

Example #3: Balancing a Pendulum in Electric Field

Practice: In the following figure, a mass m is balanced such that its tether is perfectly horizontal. If the mass is m and the angle of the electric field is 𝜃, what is the magnitude of the electric field, E?

Additional Problems
An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e., along the negative y-axis. What will be the direction of the electric force acting on the electron after entering the electric field? A) -y B) +y C) +x D) -x
A charged particle traveling along the +x axis enters an electric field directed vertically upward along the +y axis. If the charged particle experiences a force downward because of this field, what is the sign of the charge on this particle? A) It is neutral. B) It is positive. C) It is negative. D) None of previous is correct.
The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to these two charges is zero? (a) only region X (b) only regions X and Z (c) only region Y (d) only region Z (e) all three regions
Two charged particles are located at x = -a and x = +a, as shown below, on the x-axis. The electric field produced by these two charges at any point on the y-axis, is always A) in the +y direction B) in the -y direction C) in the +x direction D) in the -x direction
Two charges, q1 = -2.50 nC and q 2 = +2.00 nC, are placed 0.400 m apart as shown in the figure. What is the magnitude of the electric field at point P, 0.300 m above q 2? A) 71.9 N/C B) 218 N/C C) 53.9 N/C D) 163 N/C E) 146 N/C
Two charges, q1 = -2.50 nC and q 2 = +2.00 nC, are placed 0.400 m apart as shown in the figure. What is the direction  of the electric field at point P, 0.300 m above q 2? A) 116° counter-clockwise from the positive x-axis. B) 63.7° clockwise from the positive x-axis. C) 72.4° counter-clockwise from the positive x-axis. D) 108° clockwise from the positive x-axis. E) 90° counter-clockwise from the positive x-axis.
Two charges, q1 = 5 μC  and q 2 = 7 μC, are separated by 10 cm, with q 1 to the left of q2. Where is the net electric field, due to both charges, zero? 
A pendulum has a charged mass at the end of it, as shown in the figure below. If it is in equilibrium, what is the magnitude of the electric field?
Find the electric field at point P due to the charges shown.
Two charged metal plates in vacuum are 0.15 m apart, with an electric field between the plates of E = 3000 N/C. A proton (q= +e = 1.6x10-19 C, m = 1.67x10 -27 kg) is shot with a speed of 2x105 m/s from the positive plate. What will be its speed before hitting the negative plate?
Two point charges having charge of -6.25 x 10 -9 C and -12.5 x 10 -9 are 25.0 cm apart. a) Calculate the magnitude of Coulomb force between them. Is it repulsive or attractive? b) What is the magnitude of electric field at point A? What is its direction?  
A charge of 3 μC is at the origin. The Coulomb constant is 8.98755 × 10  9 Nm2/C2. What is the magnitude of the electric field on the x axis at x = −5 m?
A charge of 3 μC is at the origin. Sketch the function E x versus x for both positive and negative values of x. (Remember that Ex is negative when E points in the negative x direction.)
Four identical point charges, q, are placed at the corners of a square. Each side of the square has length L. What is the magnitude of the electric field at the point P, the center of the square? A) 0 B) kq2/L2 C) kq2/2L2 D) kq2/4L2  
In the figure, point  B is a distance L away from a point charge Q. Point A is a distance 4L away from Q. What is the ratio of the electric field at  A to that at  B, EA/EB? A) 1/16 B) 1/9 C) 1/4 D) 1/3 E) This cannot be determined
The four charges form a square of edge length a. What is the direction of the net electric field at the square's center? a. -x b. +x c. +y d. -y e. The field is zero at the center.
An electron traveling horizontally at 6 × 10 6 m/s enters a 0.05 m region with a uniform electric field of 89 N/C , perpendicular to the electron's velocity. The mass of an electron is 9.10939 × 10−31 kg and the charge on an electron is 1.60218 × 10−19 C . What is the magnitude of the vertical displacement ∆y of the electron while it is in the electric field? 1. 0.00485434 2. 0.000543524 3. 0.0148796 4. 0.0649004 5. 0.00403356 6. 0.000873782 7. 0.00354891 8. 0.0176498 9. 0.00427393 10. 0.00586273
Two point charges are separated by 20 cm and have charges of +8.0 and +16.0 μC, respectively. What is the electric field at a point midway between the two charges? (a) 28.8 x 106 N/C (b) 1.44 x 107 N/C (c) 7.2 x 106 N/C (d) zero+
Three point charges are placed at the vertices of an equilateral triangle. Find the magnitude of the electric field E at P. The value of the Coulomb constant is 8.9875 × 109 N · m2/C2. Answer in units of N/C. 
An electron is accelerated by a constant electric field of magnitude 208 N/C. A) Find the magnitude of the acceleration of the electron. The mass of an electron is 9.109 × 10−31 kg and the elemental charge is 1.6 × 10−19 C. Answer in units of m/s2. B) Find the electron’s speed after 1.93 × 10−8 s, assuming it starts from rest. Answer in units of m/s.  
An electron traveling at 2 × 106 m/s enters a 0.08 m region with a uniform electric field of 246 N/C , as in the figure. A) Find the magnitude of the acceleration of the electron while in the electric field. The mass of an electron is 9.109 × 10−31 kg and the fundamental charge is 1.602 × 10−19 C . Answer in units of m/s2. B) Find the time it takes the electron to travel through the region of the electric field, assuming it doesn’t hit the side walls. Answer in units of s. C) What is the magnitude of the vertical displacement ∆y of the electron while it is in the electric field? Answer in units of m.
Two unequal point charges are separated as shown in the figure. The electric field due to this combination of charges can be zero. a) Only in region 1. b) Only in region 2. c) Only in region 3. d) In both regions 1 and 3.
In the four configurations of charges, all the charges are the same magniture, Q, but can be positive or negative. The distance between adjacent items is always the same. In which situation is the magnitude of the electric field at point P the largest? A) Situation A B) Situation B C) Situation C D) Situation D
In the figure, point A is a distance L away from a point charge Q. Point B is a distance 4L away from Q. What is the ratio of the electric field at  B to that at A, EB/EA? A) 1/16 B) 1/9 C) 1/4 D) 1/3 E) This cannot be determined since neither the value of Q nor the length L is specified.
Five particles are shot from the left into a region that contains a uniform electric field. The numbered lines show the paths taken by the five particles. A negatively charged particle with a charge -3Q follows path 2 while it moves through this field. Do not consider any effects due to gravity. Which path would be followed by a charge +6Q? Path 1 Path 2 Path 3 Path 4 Path 5
Three charges are arranged along the x-axis: +q at x = -2d; +2q at x = d; –4q at x = 2d. Which expression gives the magnitude of the electric field at the origin (x = 0)? In the expressions below, the constant 1/(4πϵ0) has been replaced with k. A. 5kq / 4d2 B. 11kq / 4d2 C. 13kq / 4d2 D. 3kq / 4d2
An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e. along the negative y-axis. What will be the direction of the electric force acting on the electron after entering field?A) downwardB) upwardC) to the leftD) to the right
A charge q1 = +5.0 x 10-9 C is located at the origin of an xy-coordinate system, and a charge q2 = -2.0 x 10-9 c is located on the y-axis at y = 0.3 m. Find the components of the electric field at a point P with coordinates (0.4 m, 0.3 m).