The Formula for the Electric Field of a Point Charge

Oct 13, 2025 by leolavanderia.com.br 83 views

Understanding Electric Fields and Point Charges

Electric fields are a fundamental concept in physics, describing the force exerted on charged particles by other charged particles or objects. A point charge is a charged particle with no dimensions, and it is a common model used to study electric fields. In this article, we will explore the strength of the electric field 0.5 m from a 6 μC charge, using the formula for the electric field of a point charge.

The Formula for the Electric Field of a Point Charge

The electric field of a point charge is given by the formula:

E = k * q / r^2

where:

E is the electric field strength in N/C
k is Coulomb's constant, which is 8.99 x 10^9 N * m^2 / C^2
q is the charge in coulombs (C)
r is the distance from the charge in meters (m)

Calculating the Electric Field Strength

To calculate the electric field strength, we need to plug in the values given in the problem. The charge is 6 μC, which is equal to 6 x 10^-6 C. The distance from the charge is 0.5 m.

First, we need to calculate the value of k * q:

k * q = 8.99 x 10^9 N * m^2 / C^2 * 6 x 10^-6 C = 5.394 x 10^4 N * m^2 / C

Next, we need to calculate the value of r^2:

r^2 = (0.5 m)^2 = 0.25 m^2

Now, we can plug in the values into the formula:

E = k * q / r^2 = 5.394 x 10^4 N * m^2 / C / 0.25 m^2 = 2.1576 x 10^5 N / C

Rounding the Answer to the Nearest Whole Number

The problem asks us to round the answer to the nearest whole number. Therefore, we need to round 2.1576 x 10^5 N / C to the nearest whole number.

Rounding 2.1576 x 10^5 N / C to the nearest whole number gives us:

E ≈ 215760 N / C

Conclusion

In this article, we calculated the strength of the electric field 0.5 m from a 6 μC charge using the formula for the electric field of a point charge. We plugged in the values given in the problem and calculated the electric field strength. Finally, we rounded the answer to the nearest whole number to get the final answer.

The Final Answer

The final answer is: 215760

Understanding Electric Fields and Point Charges

Q&A: Electric Fields and Point Charges

Q: What is an electric field?

A: An electric field is a region around a charged particle or object where the force of the charge can be detected. It is a vector field that describes the force exerted on a charged particle by other charged particles or objects.

Q: What is a point charge?

A: A point charge is a charged particle with no dimensions. It is a common model used to study electric fields.

Q: What is the formula for the electric field of a point charge?

A: The formula for the electric field of a point charge is:

E = k * q / r^2

where:

E is the electric field strength in N/C
k is Coulomb's constant, which is 8.99 x 10^9 N * m^2 / C^2
q is the charge in coulombs (C)
r is the distance from the charge in meters (m)

Q: How do I calculate the electric field strength?

A: To calculate the electric field strength, you need to plug in the values given in the problem into the formula. You need to calculate the value of k * q and the value of r^2, and then divide the value of k * q by the value of r^2.

**Q: What is the value of k * q?**

A: The value of k * q is 8.99 x 10^9 N * m^2 / C^2 * 6 x 10^-6 C = 5.394 x 10^4 N * m^2 / C.

Q: What is the value of r^2?

A: The value of r^2 is (0.5 m)^2 = 0.25 m^2.

Q: How do I round the answer to the nearest whole number?

A: To round the answer to the nearest whole number, you need to look at the decimal part of the answer. If the decimal part is less than 0.5, you round down to the nearest whole number. If the decimal part is 0.5 or greater, you round up to the nearest whole number.

Q: What is the final answer?

A: The final answer is 215760 N / C.

Conclusion

In this article, we answered some common questions about electric fields and point charges. We explored the formula for the electric field of a point charge and calculated the electric field strength 0.5 m from a 6 μC charge. We also discussed how to round the answer to the nearest whole number.

The Final Answer

The final answer is: 215760