Resultant Electric field between charges

[williamhannah]

Homework Statement

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

Homework Equations

I know the eleectric field can be calculated using E = (kQ)/r^2 but I am unsure how to calculate this.

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[/B]

But I can't seem to get these answers.

 

[gneill]

Homework Statement

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

Homework Equations

I know the eleectric field can be calculated using E = (kQ)/r^2 but I am unsure how to calculate this.

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[/B]

But I can't seem to get these answers.

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.

 

[williamhannah]

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.

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.

 

[gneill]

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.

Looks good so far!

bii) I am unsure of how to do this one.

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.

 

[williamhannah]

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.

This is one that I am really unsure of

 

[Arman777]

This is one that I am really unsure of

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.