Two 16 cm -long thin glass rods uniformly charged to +18nC are placed side by side, 4.0 cm apart. What are the electric field strengths E1, E2, and E3 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?
at 1 cm mark .
a = distance of location from each rod
L = length of rod = 16 cm = 0.16 m
electric field by each rod is given as
E = kQ/(a sqrt(a2 + L2/4))
for left rod :
a1 = 1 cm = 0.01 m
Eleft = kQ/(a1 sqrt(a12 + L2/4)) = (9 x 109) (18 x 10-9)/((0.01) sqrt((0.01)2 + (0.16)2/4)) = 200936.27 N/C towards right
for right rod :
a2 = 4 - 1 cm = 3 cm = 0.03 m
Eright = kQ/(a2 sqrt(a22 + L2/4)) = (9 x 109) (18 x 10-9)/((0.03) sqrt((0.03)2 + (0.16)2/4)) = 63202.22 N/C towards left
E1 = Eleft - Eright = (200936.27) - (63202.22) = 137734.05 N/C towards right
at 2 cm mark .
for left rod :
a1 = 2 cm = 0.02 m
Eleft = kQ/(a1 sqrt(a12 + L2/4)) = (9 x 109) (18 x 10-9)/((0.02) sqrt((0.02)2 + (0.16)2/4)) = 98226 N/C towards right
for right rod :
a2 = 4 - 2 cm = 2 cm = 0.02 m
Eright = kQ/(a2 sqrt(a22 + L2/4)) = (9 x 109) (18 x 10-9)/((0.02) sqrt((0.02)2 + (0.16)2/4)) = 98226 N/C towards left
E1 = Eleft - Eright = (98226) - (698226) = 0 N/C
at 3 cm mark .
for left rod :
a1 = 3 cm = 0.03 m
Eleft = kQ/(a1 sqrt(a12 + L2/4)) = (9 x 109) (18 x 10-9)/((0.03) sqrt((0.03)2 + (0.16)2/4)) = 63202.22 N/C towards right
for right rod :
a2 = 4 - 3 cm = 1 cm = 0.01 m
Eright = kQ/(a2 sqrt(a22 + L2/4)) = (9 x 109) (18 x 10-9)/((0.01) sqrt((0.01)2 + (0.16)2/4)) = 200936.27 N/C towards left
E1 = Eleft - Eright = (63202.22) - (200936.27) = -137734.05 N/C towards left
Two 16 cm -long thin glass rods uniformly charged to +18nC are placed side by side,...
Two 16 cm -long thin glass rods uniformly charged to +18nC are placed side by side, 4.0 cm apart. What are the electric field strengths E1, E2, and E3 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?
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