Electric Field with three charges

In summary, the problem involves finding the electric field at a point to the left of three charges on a horizontal line. The values for the charges and distances are given, along with the acceleration due to gravity and Coulomb Constant. The student attempted to solve the problem by converting all units to C and meters, then calculating the electric fields for each charge and adding them together. However, the correct solution involves finding the electric fields for all three charges and taking direction into account. The final answer should have E1 and E3 as negative (pointing to the left) and E2 as positive (pointing to the right).
  • #1
rinarez7
27
0
1. Homework Statement
Consider 3 charges along a horizontal line as shown:
8.72e-6 C (+) ___4.16cm____2.45e-6 C (+)______3.18cm_____-1.46e-6C (-)
The acceleration due to gravity is 9.8 m/s^2
The Coulomb Constant is 8.98755e 9 Nm^2/ C^2
What is the electric field at a point 2.18 cm to the left of the middle charge? Answer in units fo N/C


2. Homework Equations
Q1= 8.72e-6 C , r= .0198m (.0416m-.0218m)
Q2= 2.45e-6 C, r= .0218m

E1= k Q1 / r^2
E2= k Q2/ r^2

3. The Attempt at a Solution
I converted all of my units first to C and meters.
Then I solved for E1 and E2 separately.
Once I had E1 and E2, I added the two together. But I can't seem to get the right answer.
Am I supposed to subtract them instead becasue Q1 and Q2 are both positive and therefore will repel each other?
 
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  • #2
You have THREE charges causing electric fields, so you need to find E1, E2 and E3.
Add them together, keeping direction in mind!
 
  • #3
so I calculated E1 = 1.999e8, E2 as 4.633e5, and E3 as -3.657e6
Am I correct to say then that, E1 and E3 are negative (pointing to the left) and E2 is positive?
E1(+)<----X----->E2 (+)-----><------E3 (-)
 
  • #4
E1 to the right (away from a positive charge), E2 to the left (away from a positive charge), E3 to the right (toward a negative charge).
 
  • #5
Thank you!
 

What is an electric field?

An electric field is a physical quantity that describes the effect that electrically charged objects have on each other. It is a vector field that exists in the space surrounding a charged object, and it can be thought of as the force per unit charge that a test charge would experience if placed in that field.

How is the electric field calculated?

The electric field at a point in space is calculated by dividing the force exerted on a test charge by the magnitude of the test charge. This can be represented mathematically as E = F/q, where E is the electric field, F is the force, and q is the magnitude of the test charge. For a system of multiple charges, the electric field is the vector sum of the individual electric fields from each charge.

What is the significance of a positive or negative electric field?

A positive electric field indicates that the force on a positive test charge would be in the direction of the field, while a negative electric field indicates that the force would be in the opposite direction. This can also be thought of as a repulsive or attractive force between charges. A positive electric field is created by a positively charged object, while a negative electric field is created by a negatively charged object.

What is the relationship between electric field and electric potential?

Electric potential is the potential energy per unit charge at a point in an electric field. It is directly related to the strength of the electric field, with a stronger electric field resulting in a higher electric potential. The electric field can be calculated from the electric potential using the equation E = -∇V, where ∇V is the gradient of the electric potential.

How does the presence of three charges affect the electric field?

The presence of three charges will create a more complex electric field, as the individual electric fields from each charge will interact with each other. The resulting electric field will depend on the relative positions and magnitudes of the charges. In general, the electric field will be strongest near the charges and weaker further away, but the exact shape and direction of the field will vary based on the specific arrangement of the charges.

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