Find Unknown Charge q: Two Point Charges on x-Axis

[kbyws37]

Two point charges are located on the x−axis: a charge of +7.80 nC at x = 0 and an unknown charge q at x = 0.50 m. No other charges are nearby. If the electric field is zero at the point x = 1.0 m, what is q?


I separated the charges.
q1 = +7.80 nC
q2 = unknown

I am confused about the last part of the question where the electric field is zero.

Would I use the equation
E= k(Q) / r^2

(Correct answer is: -1.95 nC)

 

[Hootenanny]

Yes you would use the definition of the electric field to set up an equation of the form;

$$E_1 + E_2 = 0$$

 

[Vagrant]

What are the electric field vectors at x=1m due to Q1 and Q2?

 

[kbyws37]

I'm not getting the right answer.
I did...

0 = ((8.99x10^9)(7.80)) / 0.5^2) + ((8.99x10^9)(q)) / 0.5^2)

which does not equal zero.

I think I still need to do something else.. something about point x = 1.0m ?

 

[Hootenanny]

Indeed, how far is the first charge (q1) located from the point of zero electric field?

 

[kbyws37]

Indeed, how far is the first charge (q1) located from the point of zero electric field?

it would be
1.0 meter

 

[Vagrant]

Check your expession for electric field due to q1.

 

[Hootenanny]

it would be
1.0 meter

That's correct, not 0.5m as you had previously