Question

a point charge is used to determine the electric field around a charged particle. why is it necessary that the point charge does not affect the position of the charge being tested?
the amount of charge will increase if the charged particle moves closer to the point charge, so any change in position changes the field.
the amount of charge will decrease if the charged particle moves closer to the point charge, so any change in position changes the field.
electric fields are inversely proportional to the square of the distance, so any change in position changes the field.
electric fields are directly proportional to distance, so any change in position changes the field.

Explanation:

1. Analyze the first option: The amount of charge on a particle doesn't increase just by moving closer to another charge, so this is incorrect.
2. Analyze the second option: Similarly, the amount of charge on a particle doesn't decrease by moving closer to another charge, so this is incorrect.
3. Analyze the third option: The formula for the electric field due to a point charge is \( E=\frac{kQ}{r^{2}} \), where \( E \) is the electric field, \( k \) is a constant, \( Q \) is the source charge, and \( r \) is the distance from the source charge. This shows that the electric field is inversely proportional to the square of the distance (\( r^{2} \)). If the test charge's position (and thus \( r \)) changes, the electric field being measured will change. So this option is correct.
4. Analyze the fourth option: From the formula \( E = \frac{kQ}{r^{2}} \), the electric field is inversely proportional to the square of the distance, not directly proportional to the distance. So this option is incorrect.

Answer:

C. Electric fields are inversely proportional to the square of the distance, so any change in position changes the field.