I think I am brain dead today. I can't even solve this simple problem

[flyingpig]

Homework Statement

A uniform electric field of magnitude 325 V/m is directed in the negative y direction in Figure P25.9. The coordinates of point A are (-0.200, -0.300) m, and those of point B are (0.400, 0.500) m. Calculate the potential difference VB - VA, using the blue path.

The Attempt at a Solution

$$\Delta V = E \cdot \Delta d$$

$$\Delta d = \sqrt{(0.4 - (-0.2))^2 + (0.5 - (-0.2))^2} = 1$$

$$\Delta V = V_b - V_a = (-325V/m)(1m) = -325V$$

Apparently the actual answer is just the vertical path, that is (-325V/m) * (-0.8m) = 260V

Now my question is, just what am I doing? I did the path from a to b and found the length to be 1.

 

[tiny-tim]

hi flyingpig!

(have a delta: ∆ and a square-root: √ )

work done is a dot product of two vectors …

∆d is a vector, not a scalar

(you can only treat force and displacement as scalars in a purely 1D situation)

 

[flyingpig]

Wait you know what I just overlooked

$$-E \cdot \Delta d = <0,-325> \cdot <0,0.8> = -260V$$

But how did the book get +260V?

 

[tiny-tim]

you've miscounted the minuses

 

[flyingpig]

What do you mean?

 

[tiny-tim]

you wrote -E in letters, but then you wrote +E in numbers

 

[flyingpig]

No I had <0,-325>

 

[gneill]

$$dV = - \vec{E} \cdot \vec{ds}$$

 

[tiny-tim]

No I had <0,-325>

that is +E

 

[flyingpig]

Is it just me or is PF laggin really hard the last two days? It almost always pops up a dead link for me.

 

[gneill]

Is it just me or is PF laggin really hard the last two days? It almost always pops up a dead link for me.

Yeah, its very, very slow, and often only gets only partway through loading a page before the browser gives up. It's almost unusable.

It looks for all the world like a denial of service attack is going on on their IP address.