# Magnitude and direction of Electric field

## Homework Statement

Calculate the magnitude of the electric field E = (-11i^+14j^)N/C

∣∣E⃗ ∣∣ = _______ N/C

Calculate the direction (relative to the +x-axis ) of the electric field E = (-11i^+14j^)N/C.

θ =_________∘ counterclockwise from the +x-axis

## The Attempt at a Solution

So magnitude would be SQRT(-11^2 + 14^2) = SQRT(317) = 17.8 N/C

For direction you'd take the inverse tan so:

theta = ATAN(14/-11) = -51.8 degrees

But that means the angle is 51.8 degrees BELOW the x-axis, so counter-clockwise it'd be

360-51.8 = 308.2 degrees
BUT I'm getting this part wrong and I don't know why? what am I doing wrong

## Answers and Replies

Chestermiller
Mentor
From the expression for the field vector in component form, it looks like the angle lies in the second quadrant.

So should i just subtract 51.8 from 180 degrees?

Chestermiller
Mentor
So should i just subtract 51.8 from 180 degrees?
Yes.

Thank you!

How do you know to find theta using arctan(14/11)? and then to subtract that from 180?