Question

A positive charge of 0.800μ C is located in a uniform field of 9.50×104 N/C. A negative charge of -0.400μ C is brought near enough to the positive charge that the attractive force between the charges just equals the force on the positive charge due to the field. How close are the two charges?

Answer 1

The force on the charge \( q \) due to the electric field is
\[ F_{field} = Eq \]

And the force on the charge \( q \) due to the second charge \( q' = -0.4 \mu C \) is the Coulomb force,
\[ F_c = \frac{kqq'}{r^2} \] where \( r \) is the distance you need to calculate.

Set the two charges equal and solve for \( r \).

Answer 2

*two FORCES equal and solve for \( r \)

Answer 3

do i find the absolute value of q' ? because I cant take the sqrt of a neg #

Answer 4

The absolute value of the two forces are equal, yes

Answer 5

I can't get the correct answer for some reason

Answer 6

If there two are equal, then
\[ Eq = kqq'/r^2 \ \implies r = \sqrt{E/k|q'|} \]

Answer 7

absolute value of the two => ...

Just make sure everything is in SI units.

Answer 8

sqrt of (9.5*10^4)*(9*10^9)*(.4*10^-6) is that right?

Answer 9

Going by the last formula that James provided, don't you need to divide the value for the electric field by k and q before squaring?

Answer 10

I'm confused

Answer 11

First, do you agree with the algebraic derivation above that
\[ r = \sqrt{\frac{E}{k|q'|}} \]

Answer 12

You should be calculating the following quantity\[r= \sqrt( 9.5\times10^{4} )/(9 \times10^{9} \times (0.4*10^{-6})) \]

Answer 13

I got 5.14 for that answer

Answer 14

I get that too. Why isn't it correct?

Answer 15

What's the official answer?

Answer 16

I am not sure it just tells me when i enter it into lon capa that it is wrong

Answer 17

Oh, I see. There's an algebraic error ... which one of you should have spotted as well!! ;-)

It is that r should be the reciprocal of that expression. So r is
\[ r = 0.195 \ m \]
Try that

Answer 18

Assuming everything is positive, if
\[ Eq = kqq'/r^2 \]
then
\[ r = \sqrt{kq'/E} \]

Answer 19

nice pick up

Answer 20

that was correct! my brain so so fried right now math is not my strengh. thank you guys for helping me through this