Electric field=0 for 2 charges

In summary, the electric field between a 6uC + charge at (0,0) and a 1uC + charge at (0,1m) is equal to 0 at a distance of 63 meters from both charges. The direction of the field will depend on the specific location of the point in relation to the two charges.
  • #1
phy43
6
0

Homework Statement


a 6uC + charge is at (0,0) and a 1uC + charge is at (0,1m). Where between them is the electric field equal to 0?


Homework Equations


F=qE
F=K(q_1)(q_2)/r^2


The Attempt at a Solution


F=K(q_1)(q_2)/r^2
F=(9.0*10^9)(1*10^-6)(6*10^-6)/(1^2)
F=5.4*10^-5 (The force each exerts upon each other)

F=qE
Since E=0, F=0

F=0 at:
0=K(q_1)(q_2)/r^2
Find r

0=(9.0*10^9)(1*10^-6)(6*10^-6)/r^2

And this is where we have a problem
 
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  • #2
You want to study the field from the two charges at various points, not the force between the two charges. Write an expression for the field at point X from each charge. Add to get the total field. (Careful with signs.)
 
  • #3
Electric field at distance r for each charge
E=Kq/r^2

E_1=(9.0*10^9)(6*10^-9)/r^2
E_1 = 54/r^2

E_2=(9.0*10^9)(1*10^-9)/r^2
E_2 = 9/r^2

E_net = E_1+E_2 = 54/r^2 + 9/r^2
E_net = (54+9)(1/r^2)
E_net = 63/r^2
0 = 63/r^2
 
  • #4
phy43 said:
Electric field at distance r for each charge
E=Kq/r^2
If a point is a distance X from charge #1, how far is it from charge #2?

E_1=(9.0*10^9)(6*10^-9)/r^2
E_1 = 54/r^2
Instead of calling the distance r, call it X. Don't plug in numbers right away. (And μC = 10^-6, not 10^-9.)

What direction is the field?

E_2=(9.0*10^9)(1*10^-9)/r^2
E_2 = 9/r^2
Instead of r, write the distance in terms of X and the distance between the charges.

What direction is the field?

Note that different directions will get different signs.
 
  • #5
Thanks, figured it out.
 

1. What does it mean when the electric field is equal to zero for two charges?

When the electric field is equal to zero for two charges, it means that the forces exerted by the two charges on each other cancel out. This can happen when the two charges have equal magnitude and opposite signs, or when they are positioned at equal distances from each other.

2. How is the electric field calculated for two charges?

The electric field between two charges is calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

3. Can the electric field be zero for more than two charges?

Yes, the electric field can be zero for any number of charges as long as their positions and magnitudes are arranged in a way that the forces cancel out. This can happen in a variety of configurations, such as a line of charges with alternating signs or a ring of charges with equal magnitudes.

4. What is the significance of an electric field being zero for two charges?

When the electric field is zero for two charges, it means that the charges are in a state of equilibrium. This is important in many practical applications, such as in electronic circuits, where the goal is to achieve a balance of charges to prevent excess current or voltage.

5. Is it possible for the electric field to be zero at all points between two charges?

No, it is not possible for the electric field to be zero at all points between two charges. The electric field is only zero at a specific point in space where the forces cancel out. In other points between the two charges, the electric field will have a non-zero value.

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