Determine the potential at x = 0

+3 votes

The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 17.8 V and b = -3.40 V/m. (a) Determine the potential at x = 0.
V

Determine the potential at x = 3.00 m.
V

Determine the potential at x = 6.00 m.
V

(b) Determine the magnitude and direction of the electric field at x = 0.

magnitude V/m
direction  

Determine the magnitude and direction of the electric field at x = 3.00 m.

magnitude V/m
direction  

Determine the magnitude and direction of the electric field at x = 6.00 m.

magnitude V/m
direction  

 

asked Jan 20, 2012 in Physics by Joey33 ~Expert~ (1,216 points)
    

1 Answer

+2 votes

Just plug in the values into the given equation to solve:

V = a + bx

a = 17.8 V and b = -3.40 V/m

 

For part A:

first part, at x = 0 you would have

V = 17.8 V + -3.40(0) = 17.8  V

similarly the next part plug in x = 3m.

V = 17.8 V + -3.40(3) = 7.6  V

and then x = 6m

V = 17.8 V + -3.40(6) = -2.6 V

 

For part B:

the formula for electric field is:

E = - dV / dx  (which means its the negative of the slope of the equation for the potential difference.

V = 17.8 V + -3.40x

So the electric field would just have magnitude of 3.4 V/m, which is the slope.

This number would be the same no matter what x it is at. and the direction is positive for all of them.

answered Jan 26, 2012 by awesome ~Expert~ (1,479 points)
edited Jan 26, 2012 by awesome



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