The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater
magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net
electric field due to these two charges is zero?
The net electric field due to these two charges will be zero in region Y.
To determine the region in which the net electric field due to the two charges is zero, we need to consider the principles of superposition. The net electric field at any point is the vector sum of the individual electric fields due to each charge.
Let's consider the three regions, X, Y, and Z:
Region X: This region is closer to charge q than charge Q. Since charge q has a smaller magnitude, it will have a larger influence on the net electric field in this region. Therefore, in region X, the net electric field will not be zero.
Region Y: This region is equidistant from both charges. The electric field due to each charge will have the same magnitude but opposite direction. Therefore, in region Y, the electric fields will cancel each other out, resulting in a net electric field of zero.
Region Z: This region is closer to charge Q than charge q. Since charge Q has a larger magnitude, it will have a larger influence on the net electric field in this region. Therefore, in region Z, the net electric field will not be zero.
Based on our analysis, the region in which the net electric field due to these two charges is zero is region Y.
To determine in which region (X, Y, Z) the net electric field due to the two charges is zero, we need to consider the properties of electric fields and the principle of superposition.
First, let's assume charge q is positive and charge Q is negative, since opposite sign charges are mentioned in the question.
According to superposition, the net electric field at a point due to multiple charges is the vector sum of the individual electric fields produced by each charge.
To find the net electric field at a point, we can calculate the electric fields produced by each charge separately and then add them vectorially:
1. In region X: Here, both charges lie on the same side of the point, so the electric fields produced by each charge will have the same direction. Therefore, it is impossible for the net electric field to be zero in region X.
2. In region Y: Here, one charge lies on each side of the point. In this case, both electric fields point towards the same side. Since the magnitude of charge Q is greater than charge q, the electric field due to charge Q will be stronger. However, since the charges have opposite signs, the electric fields produced by each charge will have opposite directions. Therefore, by adjusting the location of the point, it is possible to find a position where the two fields cancel each other out, resulting in a net electric field of zero. Thus, there is a point in region Y where the net electric field is zero.
3. In region Z: Here, both charges lie on the same side of the point, but their electric fields will have different directions due to opposite signs. Therefore, it is impossible for the net electric field to be zero in region Z.
In summary, the only region where there can be a point at which the net electric field due to these two charges is zero is region Y.