Question

A rod 14 cm long is uniformly charged and has a total chargeof -22 μc. Determine the magnitude and direction of theelectric field along the axis of the rod at a point 36 cm from itscenter.

Answer is 1.59 x 10⁶ N/C toward the rod. I need thesolution, I know the answer.

Answer 1

Concepts and reason

The concept used to solve this problem is electric field along the axis of rod at a point.

Initially use the relation between charge and length of the rod to calculate the linear charge density. Then integrate the electric field expression to solve for the electric field along the axis of rod at a point from its center. Finally substitute the values in the electric field expression to calculate the electric field along the axis of rod at a point from its center.

Fundamentals

The expression for the linear charge density is,

Here, is the linear charge density, q is the charge, and L is the length of the rod.

The expression for the electric field along the axis of rod at any point from its center is,

Here, E is the electric field, k is the Coulomb constant, is the length of the rod, and a is the position of the point on the rod.

Use the expression for the magnitude of linear charge density.

Substitute for q and for in the equation .

Use the expression of electric field along the axis of rod at any point from its center.

Integrate the electric field equation .

$=k2. $

Use the expression of electric field.

Substitute for L, for k, for a, and for in the equation .

Ans:

The electric field along the axis of rod at a point from its center is .