# Calculate R from Electric field lines.

• physics16102
In summary, the conversation discusses the problem statement of finding R in meters for an electric field produced by a point charge. The person assumes equal areas and relative strengths of 5Q and 2Q, but is unable to find the correct answer. After receiving help, they realize their mistake and solve the problem correctly using the equation E=kQ/r^2.
physics16102
1. The problem statement
The electric field E (arrows) is produced by a point charge. Find R in meters

## Homework Equations

E(due to pt charge) = kq/R^2
# of field lines/unit area represents relative field strength (only statement in my notes that seems to apply to problem)

## The Attempt at a Solution

I assumed the two areas are equal, and the relative strengths are 5Q and 2Q, respectively. Then, k5Q/(1.5)^2 = k2Q/R^2 I solved and got .77, and neither .77 or 1.5+.77 are answer choices so I am obviously wrong. This problem is obviously supposed to be very easy since it is the first one on my practice test but it is nothing like anything in the book or examples done is class so I am clueless.

If anyone knows where to start on this problem or can point me in the right direction, it would be greatly appreciated. I have access to online tutoring through cengage and two tutors were unable to help me with it so I am getting desperate.

Q is the same for both distances. It is the electric field, E=kQ/r^2 which is E=5 for r=1.5 and E=2 for r=R.

ehild

Last edited:
Thank you! My notes have Q varying with the amount of electric field lines, which is where I was mistaken. The problem makes sense now

I would first clarify the problem statement. Are we trying to find the distance R from the point charge to the areas where the electric field strength is 5Q and 2Q, respectively? Or are we trying to find the magnitude of the electric field at those points?

Assuming we are trying to find the distance R, we can use the formula E = kq/R^2, where E is the electric field strength, k is the Coulomb's constant, q is the charge of the point charge, and R is the distance from the point charge.

To find R, we can rearrange the formula to R = √(kq/E). Plugging in the values given, with k = 9x10^9 Nm^2/C^2 and q = 1C, we get R = √(9x10^9 x 1 / 5) = 6x10^8 meters. This is the distance R from the point charge to the area where the electric field strength is 5Q. Similarly, for the area where the electric field strength is 2Q, R = √(9x10^9 x 1 / 2) = 9x10^8 meters.

It is important to note that the number of field lines does not directly represent the electric field strength. The relative field strength is inversely proportional to the distance squared, as shown in the formula. Therefore, the number of field lines can only provide a general indication of the relative strength of the electric field.

## What is the purpose of calculating R from electric field lines?

The purpose of calculating R from electric field lines is to determine the distance between two charges, known as the separation distance. This distance is a crucial factor in understanding the strength of the electric field between the two charges.

## What is R in the context of electric field lines?

In the context of electric field lines, R represents the separation distance between two charges. It is typically measured in meters (m) or centimeters (cm).

## What are the steps to calculate R from electric field lines?

The steps to calculate R from electric field lines are as follows:
1. Identify the two charges and their values in Coulombs (C).
2. Determine the magnitude of the electric field between the two charges in Newtons per Coulomb (N/C).
3. Use the equation E = kQ/r², where k is the Coulomb's constant (8.99 x 10⁹ Nm²/C²), Q is the charge in Coulombs, and r is the separation distance in meters.
4. Rearrange the equation to solve for r: r = √(kQ/E).
5. Plug in the values for k, Q, and E to calculate the separation distance (R) between the two charges in meters or centimeters.

## What are some common units for R when calculating electric field lines?

The most common units for R when calculating electric field lines are meters (m) or centimeters (cm).

## What are some real-world applications of calculating R from electric field lines?

Calculating R from electric field lines is essential in understanding and designing various electrical systems, such as capacitors, conductors, and electrical circuits. It is also crucial in fields such as engineering, physics, and telecommunications. Additionally, it is used in practical applications such as determining the safe distance between power lines and buildings or calculating the range of an electric field produced by a lightning bolt.

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