# Find an expression for the electric field(Mastering Physics)

• Eric Fossum
In summary, the conversation discusses solving a problem from Mastering Physics (3rd edition) involving a thin rod with a total charge Q. The solution involves finding the electric field strength on the axis of the rod at a distance r from the center, verifying the expected behavior for large r, and evaluating the expression for a specific set of values. The conversation also mentions the importance of providing the method and reasoning behind the solution instead of just the answer.

#### Eric Fossum

I just wanted to post a solution for anyone interested. Any notes on how to solve would be nice for others.

1. Homework Statement

Mastering Physics (3rd edition) Problem 26.40

The figure (Figure 1) shows a thin rod of length L with total charge Q.

Part A) Find an expression for the electric field strength on the axis of the rod at distance r from the center.

Part B) Verify that your expression has the expected behavior if r≫L.
Express your answer in terms of variables Q, rand constants π, ε0.

Part C) Evaluate E at r = 3.6cm if L = 5.0 cm and 2.2nC .
Express your answer to two significant figures and include the appropriate units.

3. The solution
Part A)

Part B)

Part C)

It is usually more help to post the method for obtaining solutions, the reasoning etc., rather than the bare answer as you have done here.
Why are those the correct answers? How would someone figure those out for themselves?

## 1. What is the definition of electric field?

The electric field is a vector quantity that describes the strength and direction of the force experienced by a charged particle in the presence of other charged particles.

## 2. How is the electric field related to the Coulomb's Law?

The electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges, as described by Coulomb's Law.

## 3. Can you explain the equation for the electric field in mathematical terms?

The electric field is represented by the equation E = F/q, where E is the electric field, F is the force, and q is the charge. This equation can also be written as E = kQ/r^2, where k is the Coulomb's constant, Q is the source charge, and r is the distance between the source charge and the point where the electric field is measured.

## 4. How do you find the direction of the electric field at a given point?

The direction of the electric field is always in the direction that a positive test charge would move if placed at that point. This can be determined by using the principle of superposition and considering the direction of the electric forces from all nearby charges.

## 5. Can you give an example of calculating the electric field using the expression?

For example, if there is a point charge of 2 microcoulombs located 3 meters away from a test charge of 5 microcoulombs, the electric field at that point can be calculated as E = (k * 2 * 5) / (3^2) = 3.33 N/C. This means that the test charge will experience an electric force of 3.33 Newtons in the direction of the point charge.