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 = 10.4 V and b = -5.50 V/m. Determine the potential at x = 0. Determine the potential at x = 3.00 m. Determine the potential at x = 6.00 m. 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

Explanation / Answer

V = a + bx

V = 10.4 - (5.5 x)

(a)
=> x = 0

V = 10.4 - (5.5 x 0) = 10.4 V

=> x = 3 m

V = 10.4 - (5.5 x 3) = -6.1 V

=> x = 6 m

V = 10.4 - (5.5 x 6) = - 22.6 V

(b)
=> x = 0

E = V/d = 10.4 / 0 = 0 V/m

=> x = 3 m

E = V/d = -6.1 / 3 = -2.03 V/m (towards x = 3 to x = 6)

=> x = 6 m

E = V/d = -22.6 / 6

E = -3.76 V/m (towards x = 6 to x = infinity)

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