Constant Electric Field and Potential

AI Thread Summary
The discussion revolves around calculating the electric potential at point 2 in a constant electric field. Given the electric field magnitude of 59.3 V/m and the potential at point 1 as 1200 V, the user attempts to find the potential at point 2 using the integral equation for electric potential. They calculate the distance between the two points as the square root of 106 and incorporate the cosine of the angle formed. However, they arrive at an incorrect potential value of 1148 V and seek suggestions for correcting their approach. The response indicates that there may have been an error in plugging in the numbers during the calculation.
ganondorf29
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Homework Statement



The figure below shows two points in an electric field. Point 1 is at (X1,Y1) = (3,4), and point 2 is at (X2,Y2) = (12,9). (The coordinates are given in meters.) The electric field is constant with a magnitude of 59.3 V/m, and is directed parallel to the +X-axis. The potential at point 1 is 1200.0 V.

prob02a_UEcoord34129.gif




Homework Equations



Vf-Vi = -Integral from i to f (E*ds)



The Attempt at a Solution



I set Vi=1200V
E = 59.3 N/C
and tried to solve for Vf

I found the distance by making a triangle connecting the two points to be the sqrt(106) and the angle formed to be 29deg. I took the cos(29) and brought that out of the integral(Im not sure if that's right, but I saw my book take the cosine of the angle so I did too).

Vf-1200 = -59.3*cos(29)*integral(from i to f) of (ds)

I solved for Vf and got 1148 V, but that's wrong. Any suggestions
 
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ganondorf29 said:
Vf-1200 = -59.3*cos(29)*integral(from i to f) of (ds)

I solved for Vf and got 1148 V, but that's wrong. Any suggestions

Looks like you just plugged the numbers in wrong. I assume that you recognized \int_i^fds=\sqrt{106}?
 
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