# Two spheres, solve for electric field strength

• axgalloway
In summary, the electric field strength at the midpoint between two 2.0-cm-diameter insulating spheres charged to +89.0 nC and -95.0 nC respectively is 9.16 * 10^5 N/C. This can be calculated by using the formula Esphere = KQ/r^2, where K = 8.99 * 10^9, Q is the charge of the sphere, and r is the distance between the centers of the charges. It is important to carefully sketch the spheres and clearly mark all distances to avoid calculation errors.
axgalloway

## Homework Statement

Two 2.0-cm-diameter insulating spheres have a 6.50 cm space between them. One sphere is charged to + 89.0 nC, the other to - 95.0 nC.

What is the electric field strength at the midpoint between the two spheres?

Esphere = KQ/r^2
k = 8.99 * 10^9

## The Attempt at a Solution

Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (3.25*10^-2)^2 + (k*95*10^-9) / (3.25*10^-2)^2

Nasty tricky wording!
Carefully sketch the spheres and mark all the distances clearly.
Remember the wording on that force formula: "distance between the centers of the charges".

Here was my 2nd attempt at a solution
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2

axgalloway said:
Here was my 2nd attempt at a solution
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2
Actually, that solution is a calculator error.
Here was my 3rd attempt at a solution (pressing the calculator correctly this time)
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2
Correct answer = 9.16 * 10^5 N/C

Thanks for the help.

Last edited:

## 1. What are two spheres and what is the purpose of solving for electric field strength?

Two spheres refer to two charged objects, and solving for electric field strength is used to determine the force that these objects exert on each other due to their electric charges.

## 2. How is electric field strength calculated for two spheres?

The electric field strength between two spheres can be calculated using the formula E = kQ/r^2, where k is the Coulomb's constant, Q is the charge on one sphere, and r is the distance between the two spheres.

## 3. What factors affect the electric field strength between two spheres?

The electric field strength between two spheres is affected by the amount of charge on each sphere, the distance between the spheres, and the medium in which the spheres are placed.

## 4. Can two spheres have the same charge and still have an electric field between them?

Yes, two spheres with the same charge can still have an electric field between them. The strength of the electric field will depend on the distance between the spheres and the medium in which they are placed.

## 5. How is the direction of the electric field between two spheres determined?

The direction of the electric field between two spheres is determined by the direction in which a positive test charge would move if placed in the electric field. The direction is always from positive to negative charges.

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