A regular pentagon has a charge of -25 nC at each vertex as shown above. a) What

Question

A regular pentagon has a charge of -25 nC at each vertex as shown above.

a) What is the magnitude of the electric field in the center of the pentagon?

b) If one of the charges is removed from the pentagon, the magnitude of the electric field at the center of the pentagon becomes 9.0 N/C. How far are the vertices of the pentagon from the center of the pentagon?

c) When all five charges are in place what is the electric potential at the center of the pentagon?

Explanation / Answer

(a)

The electric field due to the left three charges points towards the center left charge, the field due to the right three charges points towards center right charges. Therefore, the net field will be zero.

(b)

if one of the charge is removed, then the net field at center is equal to the field due to one charge.

E=9.0 N/C

kQ/r^2=9.0 N/C

9*10^9 (25*10^-9 C) /r^2 =9.0 N/C

r=5 m

(c)

The total electric potential at center is,

V=V1+V2+V3+V4+V5

=5V'

=5 (k Q/r)

=5*9*10^9 (-25*10^-9 C)/ 5 m = -225 V

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