Question

Consider a point a (see image) which is 72 cm north of the point designated as Q with a point charge of -3.8 uC and a point b (see figure) that is 88 cm west of the same designated charge As Q (in the direction toward -x), determine the following:
a) V_ba = V_b - V_a b) E_{b -} E_a (magnitude and direction)

Answer 1

given
a = 72 cm = 0.72 m
b = 88 cm = 0.88 m
Q = -3.8 micro C

a) Vba = Vb - Va

= k*Q/b - k*Q/a

= 9*10^9*(-3.8*10^-6)/0.72 - 9*10^9*(-3.8*10^-6)/0.88

= -8636 V <<<<<-----------Answer

b) |Ea| = k*|Q|/a^2

= 9*10^9*3.8*10^-6/0.72^2

= 65972 N/C (towards south)

|Eb| = k*|Q|/b^2

= 9*10^9*3.8*10^-6/0.88^2

= 44163 N/C (towards East)

|Eb - Ea| = sqrt(Eb^2 + Ea^2)

= sqrt(44163^2 + 65972^2)

= 7.94*10^4 N/C <<<<<-----------Answer

direction : theta = tan^-1(Ea/Eb)

= tan^-1(65972/44163)

= 56.2 degrees North of East <<<<<-----------Answer