# Resultant Electric field between charges

1. Feb 27, 2017

### williamhannah

1. The problem statement, all variables and given/known data
A +15 microC point charge Q1 is at a distance of 20 mm from a + 10 microC charge Q2.
Fin the resultant electric field at:
Ai) the midpoint between the two charges
ii) at point P along the line between Q1 and Q2 which is 25 mm from Q1 and 45 mm from Q2.
bi) Explain why there is a point along the line between the two charges at which the electric field is zero
ii) Calculate the distance from this point to Q1 and to Q2
2. Relevant equations
I know the eleectric field can be calculated using E = (kQ)/r^2 but I am unsure how to calculate this.

3. The attempt at a solution
The answers at the back of the book say the answers are:
ai) 4.5 x 10^8 V/m towards Q2
ii) 2.6 x 10^ V/m away from Q1
bii) 11 mm from Q1, 9 mm from Q2

But I cant seem to get these answers.

2. Feb 27, 2017

### Staff: Mentor

Show us what you've tried, even if you haven't obtained the book's answers. No help can be offered until you show your work.

3. Feb 28, 2017

### williamhannah

For ai)
E1 = kq/d^2 = ([8.9 x10^9] x [15 x 10^-6])/(10x10^-3)^2 = 1.335 x10^ 9 V/m
E2 = kq/d^2 = ([8.9 x10^9] x [1o x 10^-6])/(10x10^-3)^2 = 8.9 x10^ 9 V/m
Enet = E1 - E2 = 4.45 x 10^8 V/m towards Q2

aii)
E1 = kq/d^2 = ([8.9 x10^9] x [15 x 10^-6])/(25x10^-3)^2 = 2.14 x10^8 V/m
E2 = kq/d^2 = ([8.9 x10^9] x [10 x 10^-6])/(45x10^-3)^2 = 4.4 x10^7 V/m
Enet = E1 - E2 = 1.7 x 10^8 V/m away from Q1

bi) Is this the idea that due to the forces having the same magnitude, but in opposite directions, the electric field is zero.
bii) I am unsure of how to do this one.

4. Feb 28, 2017

### Staff: Mentor

Looks good so far!
You'll need to write an equation for the electric field at any point along a line between the two charges. How might you specify such a point? Start with a drawing of the setup.

5. Feb 28, 2017

### williamhannah

This is one that I am really unsure of

6. Feb 28, 2017

### Arman777

Electric field can be zero only and only $\vec E_{total}=0$.So

$\vec E_{1}+\vec E_{2}=0$

Their magnitudes must be be same in this case.Logically think in which point Electric field could be 0.Deterime the distances and use the upper equation.