# Test charge velocity in Coulomb's Law

• akhila_k
In summary, Coulomb's Law accommodates for the velocity of the test charge by considering the force as a function of position rather than time.
akhila_k
The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of the test charge?

akhila_k said:
The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of the test charge?

The source charge is not just at rest, but fixed. This leads to a static (i.e. constant in time) electric field and no magnetic field associated with the source charge. The test charge is then subject to an electrostatic force only, given by Coulomb's law. This force will change over time as the test charge moves.

If the force is time varying, why doesn't time parameter appear in Coulomb's law? Or Coulomb's law give the force at what time point in test charge's motion?

akhila_k said:
If the force is time varying, why doesn't time parameter appear in Coulomb's law? Or Coulomb's law give the force at what time point in test charge's motion?
The force is a function of position, not time. If you measure the force at point A, move the charge to point B, bring it back to A some time later and remeasure, the force on the charge will have the value that you measured earlier.

## 1. What is a test charge in Coulomb's Law?

A test charge is a hypothetical charge used to measure the electric field at a specific point in space, according to Coulomb's Law. It is typically a small, positive charge that does not significantly affect the electric field of the system being studied.

## 2. How is the velocity of a test charge related to Coulomb's Law?

The velocity of a test charge does not directly affect Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. However, the velocity of a test charge can affect the magnitude and direction of the electric field it experiences.

## 3. How is the velocity of a test charge measured in Coulomb's Law experiments?

The velocity of a test charge can be measured using a variety of methods, such as using a stopwatch to time how long it takes for the charge to travel a known distance, or using specialized equipment such as a velocity meter or an oscilloscope.

## 4. Can the velocity of a test charge be varied in Coulomb's Law experiments?

Yes, the velocity of a test charge can be varied in Coulomb's Law experiments by adjusting the force applied to the charge or by changing the distance between the charges. However, it is important to note that the velocity of a test charge should not be too high, as it can significantly affect the results of the experiment.

## 5. How does the velocity of a test charge affect the accuracy of Coulomb's Law?

The velocity of a test charge can affect the accuracy of Coulomb's Law if it is too high, as it can cause the charge to experience significant electromagnetic effects that can distort the results. Therefore, it is important to carefully control and measure the velocity of the test charge in order to obtain accurate results.

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