Determine the Electric Field

Homework Statement

An electric field with a magnitude of 2.5N directed to the left, acts on a negative charge of -5.0C. Determine the electric field in which the charge is located.

Give. FE=2.5N
q=-5.0C

FE[/B]=qε

The Attempt at a Solution

ε[/B]=2.5N/5.0C=0.5N/C. I don't know how to find the direction. The answer is 0.5N/C,
but I don't know how to get that direction. I guess we have to assume the positive test charge is to the right of q and figure out the direction it would move as a result of FE applied on it by q. That doesn't really make sense though.

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blue_leaf77
Homework Helper
Use vector equation ##\mathbf F = q \mathbf E##. With ##\mathbf F = -2.5 \hat x## and ##q = -5\hspace{2mm} C##, solve for ##\mathbf E##.

Use vector equation ##\mathbf F = q \mathbf E##. With ##\mathbf F = -2.5 \hat x## and ##q = -5\hspace{2mm} C##, solve for ##\mathbf E##.
I did, but I don't know how to find the direction

blue_leaf77
Homework Helper
You did, then please write out your answer for ##\mathbf E##, note that the bold symbol denotes vector notation so your answer must consist of a number and the unit vector.

You did, then please write out your answer for ##\mathbf E##, note that the bold symbol denotes vector notation so your answer must consist of a number and the unit vector.
Ok, and how do you find the direction?

blue_leaf77
Homework Helper
If you really have calculated ##\mathbf E##, not just ##|\mathbf E|##, then show it in your next comment.

If you really have calculated ##\mathbf E##, not just ##|\mathbf E|##, then show it in your next comment.
My teacher said you're not supposed to plug in - signs into the equations for fields because it implies direction, so we only use magnitudes

blue_leaf77
Homework Helper
I don't know in which manner your teacher wants you to find the direction, but the formal way is to use the vector equation. Alternatively, you can use the definition of negative charge. A negative charge is defined to be the condition such that the field the particle is exposed to exert a force in an opposite direction to that field.

I don't know in which manner your teacher wants you to find the direction, but the formal way is to use the vector equation. Alternatively, you can use the definition of negative charge. A negative charge is defined to be the condition such that the field the particle is exposed to exert a force in an opposite direction to that field.
I'm confused about the wording of the question. Usually we use a positive test charge along with the given charge. Is the test charge applying the force on q? Then it would be to the right of q since the force is directed to the left. And then q would move to the right as it is attracted by the positive test charge?

blue_leaf77
Homework Helper
Then it would be to the right of q since the force is directed to the left.
That's indeed the definition of negative charge when applied to the current problem at hand.
And then q would move to the right as it is attracted by the positive test charge?
No, the charge will move in the same direction as the force, not the field.

That's indeed the definition of negative charge when applied to the current problem at hand.

No, the charge will move in the same direction as the force, not the field.