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 = 16.6 V and b = -6.10 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.

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

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

Full, detailed solutions please!

Explanation / Answer

a)

Here ,

potential is given as

V = 16.6 - 6.10 * x

at x = 0

V = 16.6 V

at x = 3 m

V = 16.6 - 6.1 * 3

V = -1.7 V

the potential at x = 3 is -1.7 V

at x = 6 m

V = 16.6 - 6.1 * 6

V = -20 V

the potential at x = 6 is -20 V

b)

as E = -dV/dx i

E = -d/dx(16.6 - 6.10 * x) i

E = 6.1 i V/m

hence , the electric field is constant in the region

the electric field at x = 0 is 6.1 V/m in + x direction

the electric field at x = 3 is 6.1 V/m in + x direction

the electric field at x = 6 is 6.1 V/m in + x direction

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