Question

Two 18cm -long thin glass rods uniformly charged to +16nC are placed side by side, 4.0 cm apart.What are the electric field strengths E1,E2,and E3 at distances 1.0cm, 2.0cm,  and 3.0 cm to the right of the rod on the the left, 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

E2Specify the electric field strength E3.

E.

E 1

Answer 1

Step 1:

Length of the rod is .

Charge on each glass rod is .

Distance between two glass rods is .

Electric field strengths   and are placed at and to the right of left side rod by connecting mid points of two rods.

Diagram of the situation:

Electric field strength at a point located at a distance from  the center of the rod (of length  and uniform charge )along its perpendicular bisector is .

Step 2:

Field strength on each position is resultant of both left and right rods.

(i)

Find Electric field strength at the position  .

Electric field strength Contribution of left rod:

Distance from the left rod to  the position   is .

Substitute corresponding values in the formula.

.

Electric field strength Contribution of right rod:

Distance from the left rod to  the position   is .

Substitute corresponding values in the formula.

.

Direction of field strength of right rod is in opposite to that of field strength of left rod.

Thus, .

Electric field strength at the position   is .

Solution:

(i) Electric field strength at the position   is .

Answer 2

(ii)

Find Electric field strength at the position  .

 is exactly midpoint between the two rods.

Since mid point is considered , the magnitude of the right rod contribution is also same as the left rod and is in opposite direction.

.

Electric field strength at the position   is .

Answer 3

(iii)

Find Electric field strength at the position  .

Electric field strength Contribution of left rod:

Distance from the left rod to  the position   is  .

Substitute corresponding values in the formula.

.

Electric field strength Contribution of right rod:

Distance from the right rod to  the position   is  .

Substitute corresponding values in the formula.

.

Direction of field strength of right rod is in opposite to that of field strength of left rod.

Thus, .

Electric field strength at the position   is .