Electrostatic force,electric field,electric potential,electric flux

In summary, for part A, the magnitude of the electric force at the center of the cube is 200.08 dyne, with components of -200.08 dyne in the x-axis and -200.08 dyne in the y-axis. For part B, the magnitude of the electric field at the center of the cube is 8x10^-7 C/8.85x10^-12 C^2/Nm^2, or 90,395.48 Nm^2/C. For part C, the electric potential is 113.12 dyne. cm, and the work done is 113.12 dyne. cm x 1000 sc = 113,120 dyne. For
  • #1
jasonlewiz
3
0
Cube: 10 cm each side

Each q at the corner of the cube is +100 sc.

Find:

a) magnitude and direction of the electrostatic force at the center of the cube.
b) magnitude and direction of the electric field at the center of the cube of tq in place at this pt.
c) find the electric potential and work done if tq of 1000 sc is placed at the center of the cube.
d) what is the electric flux at the center of the cube.


My Solution:

a)

Sq1q9 = square root of (5 cm)^2+(5 cm)^2 = 7.07 cm
S29,S39,S49,S59,S69,S79,S89= 7.07 cm

Fq1q9=k[q1q9/(s19)^2 =1 dyne cm^2/sc^2[(100sc)(100sc)/(7.07cm)^2] = 200.08 dyne
Fq29,Fq39,Fq49,Fq59,Fq69,Fq79,Fq89= 200.08 dyne

x and y components

x axis

Fq19 = -200.08 dyne
Fq29 = 0
Fq39 = 200.08 dyne
Fq49 = 0
Fq59 = 0
Fq69 = 200.08 dyne
Fq79 = 0
Fq89 = -200.08 dyne

y axis


c. V= 1 dyne cm^2/sc^2(100/7.07)x8
V= 113.12 dyne. cm

d. Eq = 800 sc x 1 C/1x10^9 sc = 8x10^-7 C

electric flux = 8x10^-7 C/8.85x10^-12 C^2/Nm^2
electric flux = 90,395.48 Nm^2/C

I can't answer letter a and b because I don't know how will I draw the free bodied diagram of it. I attach a drawing so you can see where I place the charges. I hope you can help me :) thanks
 

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  • #2
Try to imagine the filed at the center due to one of the charges and see if gets canceled due to the field of any other charge.
 
  • #3
the wording is wrong, i think. part A must involve a tq, and part B cannot. additionally, you do not want to calculate S19, S29, etc. rather, you want S1C (distance from 1 to center of cube), S2C, etc.

however, as graphene mentioned, this is a very tedious way to solve parts A and B. It is easier to use symmetry arguments.
 

1. What is electrostatic force?

Electrostatic force is the force of attraction or repulsion between electrically charged particles. It is caused by the interaction of electric charges and is one of the fundamental forces in nature.

2. How is electric field defined?

Electric field is a physical quantity that describes the strength and direction of the force that a charged particle would experience at any given point in space. It is defined as the force per unit charge.

3. What is electric potential?

Electric potential is a measure of the potential energy per unit charge that a particle would have at a given point in an electric field. It is similar to gravitational potential energy, but in the context of electric charges.

4. What is electric flux?

Electric flux is a measure of the flow of electric field lines through a given surface. It is proportional to the number of electric field lines passing through the surface and is a key concept in understanding the behavior of electric fields.

5. How are electric field, electric potential, and electric flux related?

Electric field, electric potential, and electric flux are all related to each other through fundamental equations in electromagnetism. Electric field is the gradient of electric potential, and electric flux is the integral of electric field over a given surface.

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