Electric Potential## Homework Solution

25.36The potential is a region between x = 0 and x = 6.0 m is V = a + b x where a = 10 V and b = - 7.0 V/m. Determine

(a) the potential at x = 0, 3.0 m, and 6.0 m and

(b) the magnitude and direction of the electric field at x = 0, 3.0 m, and 6.0 m.V(x) = 10 V + ( - 7 V/m) (x)

V(0) = 10 V + ( - 7 V/m) (0)

V(0) = 10 VV(3.0 m) = 10 V + ( - 7 V/m) (3.0 m)

V(3.0 m) = 10 V - 21 V

V(3.0 m) = - 11 VV(6.0 m) = 10 V + ( - 7 V/m) (6.0 m)

V(6.0 m) = 10 V - 42 V

V(6.0 m) = - 32 VE = - dV/dx

E = - d(a + bx) / dx

E = - [da/dx + d(bx)dx]

E = - [ 0 + b ]

E = - b = constant

E = - ( - 7 V/m )

E = 7 V/mand this is the value of E for x = 0, x = 3.0 m, and x = 6.0 m; the electric field is

constant.

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