Four charges are arranged at the corners of a square as shown. Q1 is at (-L/2,L/

Question

Four charges are arranged at the corners of a square as shown. Q1 is at (-L/2,L/2), Q2 is at (L/2,L/2), point a is at the origin and Q1 is positive and Q1=Q2=-Q3=-Q4. Indicate TRUE or FALSE for each of the following statements.
a) At point a, the electric field points toward point c
b) At c, the electric field is parallel to the x axis.
c) The potential at a is greater (more positive) than the potential at c.
d) The potential at b is zero.
e) At point b, the electric field is zero.
f) The magnitude of the electric field at b is greater than at c
g) The points a, b, and c each lie on a different eqiopotential surface.

Explanation / Answer

a)

at "a" , E1 and E4 points in same direction and so does E2 and E3 . since all the charges have same magnitude and are at same distance from "a" . the magnitude of E1 , E2 , E3 and E4 is same. the X-component of E2 + E3   cancel out the X-component of E1 + E4

b)

False

at C , E2 and E4 has same magnitude horizontal component of E4 in left direction cancel out the horizontal component of E2 in right direction.   similarly,

E1 and E3 has same magnitude horizontal component of E3 in left direction cancel out the horizontal component of E1 in right direction

c)

False

at a : V1 , V2 = Positive    and V3 , V4 = negative . since all charge have same magnitude and are at same distance from "a" , they have same magnitude of electric potential at "a"

so V1 = V2 = - V3 = - V4

Va = total electric potential at "A" = V1 + V2 + V3 + V4 = 0

At c : V2 = -V4 since Q2 and Q4 are at same distance from "c"

V1 = - V3 since Q1 and Q3 are at same distance from "c"

Vc = total electric potential at "C" = V1 + V2 + V3 + V4 = 0

d)

True

e)

False

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