Question

A 10-cm-long thin glass rod uniformly charged to 15.0 nC and a 10-cm-long thin plastic rod uniformly charged to - 15.0 nC are placed side by side, 4.20 cm apart. What are the electric field strengths E1 to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods?

Specify the electric field strength E1

Specify the electric field strength E2

Specify the electric field strength E3

Answer 1

Electric field by a charged rod at a distance of 'r' on its perpendicular bisector is given as

E = k (2Q)/ (r sqrt(L² + 4r² ))

Given that Q = 15 x 10^-9 C

L = 10 cm = 0.10 m

When r = 1 cm for one rod ::

Electric field by positively charges rod on left :

E_left = k (2Q)/ (r sqrt(L² + 4r² ))                  towards right

Electric field by negatively charged rod on right :

E_right = k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))                  towards right

net Electric field E₁ is given as

E₁ = E_left + E_right

E₁ = k (2Q)/ (r sqrt(L² + 4r² )) + k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))  

E₁ = (9 x 10⁹) (2 x 15 x 10^-9) (1/((0.01) (sqrt(0.1² + 4 (0.01)²))) + 1/((0.042 - 0.01) (sqrt(0.1² + 4 (0.042 - 0.01)²)))

E₁ = 3.4 x 10⁵ N/C

When r = 2 cm for one rod ::

Electric field by positively charges rod on left :

E_left = k (2Q)/ (r sqrt(L² + 4r² ))                  towards right

Electric field by negatively charged rod on right :

E_right = k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))                  towards right

net Electric field E₁ is given as

E₂ = E_left + E_right

E₂ = k (2Q)/ (r sqrt(L² + 4r² )) + k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))  

E₂ = (9 x 10⁹) (2 x 15 x 10^-9) (1/((0.02) (sqrt(0.1² + 4 (0.02)²))) + 1/((0.042 - 0.02) (sqrt(0.1² + 4 (0.042 - 0.02)²)))

E₂ = 2.4 x 10⁵ N/C

When r = 3 cm for one rod ::

Electric field by positively charges rod on left :

E_left = k (2Q)/ (r sqrt(L² + 4r² ))                  towards right

Electric field by negatively charged rod on right :

E_right = k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))                  towards right

net Electric field E1 is given as

E₃ = E_left + E_right

E₃ = k (2Q)/ (r sqrt(L² + 4r² )) + k (2Q)/ ((0.042 - r) sqrt(L² + 4(0.042 - r)² ))  

E₃ = (9 x 10⁹) (2 x 15 x 10^-9) (1/((0.03) (sqrt(0.1² + 4 (0.03)²))) + 1/((0.042 - 0.03) (sqrt(0.1² + 4 (0.042 - 0.03)²)))

E₃ = 2.96 x 10⁵ N/C