Chapter 18, Problem 1RQ

Review Question 18.1 How do you estimate the direction of the $\stackrel{\to }{E}$ field at a point located near two point-like charged objects?

To determine

The way to estimate the direction of $\overrightarrow{E}$ at a point located near two point-like charged objects.

Answer to Problem 1RQ

Solution:

The direction of the electric field near the two-point charged objects can be estimated by knowing the sign of charge of the charged object and using the law of vector addition in the direction of electric field due to an individual object.

Explanation of Solution

Introduction:

The direction of the electric field near any charged particle can be found by knowing the direction of the electrostatic force experienced by a positive test charge at that point. A test charge is considered to have a unit magnitude.

Explanation:

The direction of the electric-field near two point-like charged objects can be estimated by knowing the sign of the charge on the charged objects.

Place a test charge at the location where the electric field has to be determined. Three possibilities arise:

1. When both the charges are positive, then the test charge is repelled by the charges. So, the electric field due to an individual charge is radially outwards along the line joining the test charge with the respective charged object. The resultant direction of the electric field can be estimated by using the law of vector addition.

2. When both the charges are negative, then the test charge is attracted by the charges. So, the electric field due to an individual charge is radially inwards along the line joining the test charge with the respective charged object. The resultant direction of the electric field can be estimated by using the law of vector addition.

3. When one charge is positive and the other is negative, then the electric field experienced by the test charge due to the positive charge is radially outwards along the line joining the positively charged object with the test charge and the electric field due to the negatively charged object is radially inwards along the line joining the negatively charged object with the test charge. The resultant direction of the electric field can be estimated by using the law of vector addition.

Conclusion:

The direction of the electric field at a point near two point-like charged objects depends on the sign of the two charges.