In the diagram below each unit on the horizontal axis is 5.00 cm and each unit o

Question

In the diagram below each unit on the horizontal axis is 5.00 cm and each unit on the vertical axis is 3.00 cm. The equipotential lines in a region of uniform electric field are indicated by the blue lines. (Note that the diagram is not drawn to scale.)

I think it's 30.96. With that, I'm supposed to find the value of FG, and then find the V corresponding to the distance of FG, then calculate V/d to get the magnitude. I can't get beyond finding the angle.

Then, for part (c), "The distance FG from part (b) corresponds to a potential difference of 18 V. What distance would a potential difference of 3 V correspond to?" Please help!

Explanation / Answer

Here, from the right-angled triangle at the origin -

tan theta = 3 / 5 = 0.6

=> theta = tan^-1(0.6) = 30.96 deg (as you find out)

This can be approximated as 31 deg.

Now the distance between the two equipotential line 's' can be determined by drawing perpendicular from one line to another.

and we have the relation -

cos (90 - 31) = d / 5

=> d = 5*cos59 = 2.57 cm

So, electric field = delta V / d = 6 / (2.57x10^-2) = 233.5 V/m

(b) again as per the condition -

2.57 cm is a 6V change then

3V change is 2.57/2 = 1.285 cm = 12.85 mm

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