A point charge q1 = -2.5 μ C is placed at x = 0 and y = +5...

A point charge $q_1 = -2.5 \mu C$ is placed at $x = 0$ and $y = +5$ cm. A second point charge $q_2 = -3 \mu C$ is placed at $x = +5$ cm and $y = 0$. Determine the magnitude of the net electric field at the origin and the direction of the electric field as an angle measured from the $+x$ axis. Use $k = 9.00 \times 10^9 \text{ N} \cdot m^2/C^2$. Magnitude = 16600000 N/C Direction = 12.5 $^\circ$ from $+x$ axis

Transcript

00:01 Alright, so let's say we have our coordinate system like this and we have a point charge placed at here.

00:08 Let's call this q1 and has a magnet or a charge of negative 1 microculems.

00:13 And then we have another charge placed here.

00:17 And this is 5 centimeters.

00:20 This is also 5 centimeters.

00:23 And this charge q2 has a charge of negative 4 .5 microculems.

00:28 So we want to know what is the electric field? at the origin, the magnitude in the direction.

00:36 So, let's, the electric field is just going to be the sum of the electric fields due to charge one and charge two at the location that we're talking about.

00:47 So it's going to be kulams constant, which we can factor out, times q1, and then we'll multiply this by a vector pointing from charge one to the origin.

01:02 Although q1 is negative, keep in mind, so we'll plug that in, and then divide it by the distance between that and the origin cubed.

01:09 And then this is like to be plus q2 times r2 over r2 cubed.

01:17 Right.

01:18 So if we plug this in, k will have 9 times 10 to the 9th newton's times the square meter per koulem squared.

01:27 And then times we'll have negative 10 to the 6th 10 to the negative 6 coulams excuse me times our vector which you know points to the point of interest so it'll point like towards the charge so it will be negative or sorry 0 and then negative 0 .05 meters and then this is divided by 0 .05 meters cubed because that's our magnitude of that distance.

02:03 And then plus, which is really going to be a negative sign because our chart is negative 4 .5 times 10 to the negative 6th kulams, times another vector that is pointing to the origin as well.

02:15 So this will be negative 0 .05 meters and 0 and then over 0 .05 meters cubed...

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