Answer:
(a) 0.2 m
(b) 3.744 x 10^6 N/C Rightwards
Explanation:
q1 = 21 micro Coulomb = 21 x 10^-6 C
q2 = 47 micro Coulomb = 47 x 10^-6 c
r = 0.5 m
(a) Let the electric field is zero at a distance d at point P from the 21 micro Coulomb.
Electric field at P due to charge q1

Where, K is Coulomb constant = 9 x 10^9 Nm^2/C^2

..... (1)
Electric field at P due to charge q2


..... (2)
Equate the equation (1) and equation (2), we get
1.496 d = r - d
1.496 d = 0.5 - d
2.496 d = 0.5
d = 0.2 m
(b) Let E1 be the electric field due to q1 at mid point P and E2 be the electric field due to q2 at mid point P.

E1 = 3024 x 10^3 N/C

E2 = 6768 x 10^3 N/C
The resultant electric field is
E = E2 - E1 = (6768 - 3024) x 10^3 = 3.744 x 10^6 N/C Rightwards