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16-2 Electric Field
Vocabulary Electric Field: An area of influence around a charged object. The magnitude of the field is proportional to the amount of electrical force exerted on a positive test charge placed at a given point in the field.
electric field or E
The SI unit of electric field is the newton per coulomb (N/C).
The electric field around a charged object is a vector and can be represented with electric field lines that point in the direction of the force exerted on a unit of positive charge. In other words, electric field lines point away from a positive charge and toward a negative charge, as shown in the diagram.
F
q o
electric force test charge
For a point charge (or other spherical charge distribution), the magnitude of the electric field can be written as
E
where q is the charge on the surface of the object, and d is the distance between the center of the charged object and a small positive test charge, q o, placed in the field.
kq
d^2
kq o q q o d^2
F
q o
Solved Examples
Example 3: Deepika pulls her wool sweater over her head, which charges her body as the sweater rubs against her cotton shirt. a) What is the electric field at a location where a 1.60 10 ^19 C-piece of lint experiences a force of 3.2 10 ^9 N as it floats near Deepika? b) What will happen if Deepika now touches a conductor such as a door knob?
a. Given: q o 1.60 10 ^19 C Unknown: E ? F 3.2 10 ^9 N Original equation: F q o E
Solved: E 2.0 1010 N/C
b. She will reduce her charge in a process called grounding, in which excess electrons flow from her body into the ground and spread evenly over the surface of Earth.
Example 4: A fly accumulates 3.0 10 ^10 C of positive charge as it flies through the air. What is the magnitude and direction of the electric field at a location 2.0 cm away from the fly?
Solution: First, convert cm to m. 2.0 cm 0.020 m
Given: k 9.0 109 N m^2 /C 2 Unknown: E ? q 3.0 10 ^10 C Original equation: E d 0.020 m
Solve: E 6800 N/C away from the fly
1 9.0 109 N #^ m^2 >C^2 2 13.0 10 ^10 C 2 1 0.020 m 22
kq d^2
kq d^2
3.2 10 ^9 N
1.60 10 ^19 C
F
q o
E 1 kq 1 /d^2 (9.0 109 N m^2 /C 2 )(6.0 10 ^6 C)/(0.15 m) 2 24 105 N/C to the right E 2 kq 2 /d^2 (9.0 109 N m^2 /C 2 )(4.0 10 ^6 C)/(0.25 m) 2 5.8 105 N/C to the left E T E 1 E 2 24 105 N/C 5.8 105 N/C 18 105 N/C to the right
18 10 5 N/C to the right
Exercise 9: April is decorating a tree in her backyard with plastic eggs in preparation for Easter. She hangs two eggs side by side so that their centers are 0.40 m apart. April rubs the eggs to shine them up, and in doing so places a charge on each egg. The egg on the left acquires a charge of 6.0 10 ^6 C while the egg on the right is charged with 4.0 10 ^6 C. What is the electric field at a point 0.15 m to the right of the egg on the left?
Answer:
