Point charges of 21.0 μc and 47.0 μc are placed 0.500 m apart. (a) at what point (in m) along the line connecting them is the electric field zero? (b) whai is the magnitude (in n/c) and direction of the electrci field halfway between them?

a) x = 0.200 m

b)E = 3.84*10^{-4} N/C

Explanation:

DISTANCE BETWEEN BOTH POINT CHARGE = 0.5 m

by relation for electric field we have following relation

according to question E = 0

FROM FIGURE

x is the distance from left point charge where electric field is zero

solving for x we get

x = 0.200 m

b)electric field at half way mean x =0.25

E = 3.84*10^{-4} N/C

(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