The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a =

Question

The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 19.2 V and b = -7.90 V/m. (a) Determine the potential at x = 0. 19.2 V Determine the potential at x = 3.00 m. X Make certain you are using the parameters a and b in the equation for V(x) correctly. V Determine the potential at x = 6.00 m. X You have been given an explicit expression for a function V(x). How do you find the value of this function at a particular point? V (b) Determine the magnitude and direction of the electric field at x = 0. magnitude 0 X There is no reason to assume that the electric field is zero at the origin. V/m direction +x Determine the magnitude and direction of the electric field at x = 3.00 m. X magnitude Do you know of an example in which the electric potential is linear? What electric field generates such a potential? V/m direction +x Determine the magnitude and direction of the electric field at x = 6.00 m. magnitude X If you know the electric potential in a region of space, how do you find the electric field there? V/m direction +x

Explanation / Answer

A) at x = 0

v = a+bx = a = 19.2 V

at x = 3m

V = 19.2-(7.9*3) = -4.5 V

at x = 6 m

V = 19.2-(7.9*6) = -28.2 V

B) Electric field E = dV/dx = (d/dx)(a+bx) = b

at x= 0

E = -7.9 V/m

at x = 3

E = -7.9 V/m

at x = 6m

E = -7.9 V/m

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