Question

The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 10.6 V and b = -4.90 V/m. (a) Determine the potential at x = 0. 10.6 Correct: Your answer is correct. V Determine the potential at x = 3.00 m. V (b) Determine the magnitude and direction of the electric field at x = 0. magnitude 4.9 Correct: Your answer is correct. V/m direction +x Correct: Your answer is correct. Determine the magnitude and direction of the electric field at x = 3.00 m. magnitude V/m direction

Answer 1

Answer:

a) 10.6V

b) E = 4.9V/m, +x direction

c) E = 4.9V/m, +x direction

Explanation:

You have the following function:

$V=a+bx$  (1)

for the potential in a region between x=0 and x=6.00 m

a = 10.6 V

b = -4.90V/m

$V=10.6V-4.90\frac{V}{m}x$

a) for x=0 you obtain for V:

$V=10.6V-4.90\frac{V}{m}(0m)=10.6V$

b) The relation between the potential difference and the electric field can be written as:

$E=-\frac{dV}{dx}=-b=-(-4.9V/m)=4.9V/m$  (2)

the direction is +x

c) The electric field is the same for any value of x between x=0 and x=6m.

Hence,

E = 4.9V/m, +x direction