Two 13 cm-long thin glass rods uniformly charged to +14nC are placed side by sid

Question

Two 13 cm-long thin glass rods uniformly charged to +14nC are placed side by side, 4.0 cm apart. What are the electric field strengths E_1, E2_, and E_3 at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left, along the line connecting the midpoints of the two rods? Specify the electric field strength E_1. Express your answer to two significant figures and include the appropriate units. Specify the electric field strength E_2. Express your answer to two significant figures and include the appropriate units. Specify the electric field strength E_3. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

At 1 cm mark :

aleft = distance of left plate = 0.01 m

aright = distance of right plate = 0.03 m

Eleft = electric field by left plate = 2kQ/(aleft sqrt(L2 + 4aleft2))

Eleft = 2 (9 x 109) (14 x 10-9)/((0.01) sqrt((0.13)2 + 4(0.01)2)) = 1.95 x 105 to right

Eright = electric field by right plate = 2kQ/(aright sqrt(L2 + 4aright2))

Eright = 2 (9 x 109) (14 x 10-9)/((0.03) sqrt((0.13)2 + 4(0.03)2)) = 5.87 x 104 to left

Net electric field is given as

E1 = Eleft - Eright = (1.95 x 105) - (5.87 x 104) = 1.36 x 105 N/C

At 2 cm mark :

aleft = distance of left plate = 0.02 m

aright = distance of right plate = 0.02 m

Eleft = electric field by left plate = 2kQ/(aleft sqrt(L2 + 4aleft2))

Eleft = 2 (9 x 109) (14 x 10-9)/((0.02) sqrt((0.13)2 + 4(0.02)2)) = 9.3 x 104 to right

Eright = electric field by right plate = 2kQ/(aright sqrt(L2 + 4aright2))

Eright = 2 (9 x 109) (14 x 10-9)/((0.02) sqrt((0.13)2 + 4(0.02)2)) = 9.3 x 104 to left

Net electric field is given as

E2 = Eleft - Eright = (9.3 x 104) - (9.3 x 104) = 0 N/C

at 3 cm mark :

aleft = distance of left plate = 0.03 m

aright = distance of right plate = 0.01 m

Eleft = electric field by left plate = 2kQ/(aleft sqrt(L2 + 4aleft2))

Eleft = 2 (9 x 109) (14 x 10-9)/((0.03) sqrt((0.13)2 + 4(0.03)2)) = 5.87 x 104 to left

Eright = electric field by right plate = 2kQ/(aright sqrt(L2 + 4aright2))

Eright = 2 (9 x 109) (14 x 10-9)/((0.01) sqrt((0.13)2 + 4(0.01)2)) = 1.95 x 105 to left

Net electric field is given as

E1 = Eleft - Eright = (- 1.95 x 105) + (5.87 x 104) = - 1.36 x 105 N/C

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