Question

A -15nC charge is located at (x, y) = (1.2cm , 0 cm).

What is the x-component of the electric field at the position (x, y) = (0 cm, 4.0cm )?

What is the y-component of the electric field at the position (x, y) = (0 cm, 4.0cm )?

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps plz rate

a) The field points to the left (-i direction, no y component). The field from the charge is radially outwards, so the point's y-coordinate must be 2cm (same as the charge), and the point must be to the left of the charge. You need to draw a diagram to see this clearly; mark the points and some outward pointing radial field lines from the charge and it should be clear.

If the distance from point to the charge is d, then E = kq/d^2
225000 = 8.99x10^9 x (12.7x10^-9) / d^2
d^2 = 5.07x10^-4
d = 0.023m = 2.3cm
So the point is 2.3cm to left of the charge, x = 1-2.3 =-1.2cm
Coordinates (-1.2cm, 2cm)
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b) For this one we start by finding the resultant field - its magnitude and direction. I assume you know how to combine the vector components of 161000i + 80500j N/C:
Resultant = sqrt(161000^2+80500^2)
= 180,000 N/C
Direction of field = tan-1(80500/161000) = tan-1(0.5) =26.6degrees

If the distance from point to charge is d, then E = kq/d^2
180000 = 8.99x10^9 x (12.7x10^-9) / d^2
d^2 = 6.34x10-4
d = 0.025m = 2.5cm
Again you need a diagram.
The x displacement of the point from the charge =2.5cos(26.6) = 2.2cm
The y displacement of the point from the charge =2.5sin(26.6) = 1.1cm

The point must be to the right and above the charge to have both components positive (which you can see on a diagram showing the radial outwards field).
So the coordinates of the point are ((1+2.2)cm, (2+1.1)cm) = (3.2cm, 2.1cm)

You do c) in a similar way to b), noting the point must be to the right and below the charge (21600i -28800j N/C has positive x-component of field and a negative y-component of field) - you should draw a suitable diagram to see this.