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?

Only region X

To determine the regions where the net electric field due to two unequal point charges is zero, we need to consider the charge signs and magnitudes.

1. If the charges q and Q have the same sign:
- Region X: In this region, the electric field due to both charges will point away from charge q and towards charge Q. Therefore, there won't be a point where the net electric field is zero.

- Region Y: In this region, the electric field due to both charges will point away from charge q and towards charge Q. Therefore, there won't be a point where the net electric field is zero.

- Region Z: In this region between the charges, the electric field due to charge q will point away from it, and the electric field due to charge Q will point towards it. At some point between the charges, the magnitudes of the electric fields due to charges q and Q will be equal and cancel each other out. This will result in a net electric field of zero.

2. If the charges q and Q have opposite signs:
- Region X: In this region, the electric field lines due to charge q will point towards it, while the electric field lines due to charge Q will point away from it. At some point between charges q and Q, the magnitudes of the electric fields due to both charges will be equal and opposite, resulting in a net electric field of zero.

- Region Y: In this region, the electric field lines due to charge q will point towards it, while the electric field lines due to charge Q will point away from it. At some point between charges q and Q, the magnitudes of the electric fields due to both charges will be equal and opposite, resulting in a net electric field of zero.

- Region Z: In this region between the charges, the electric field due to charge q will point towards it, and the electric field due to charge Q will also point towards it. Therefore, there won't be a point where the net electric field is zero.

To summarize, in the case where the charges q and Q have opposite signs, the net electric field will be zero in regions X and Y.

To determine in which regions there will be a point where the net electric field due to the two charges is zero, we need to analyze the forces they exert on one another.

Region X: This region is to the right of the charges. Here, both charges are pushing away from each other, so it is unlikely that there will be any point where the net electric field is zero.

Region Y: This region is between the charges. Here, the electric field due to Q will be directed towards the right, while the electric field due to q will be directed towards the left. Since Q has a greater magnitude, the net electric field will be directed towards the right. Therefore, it is unlikely for there to be a point where the net electric field is zero in this region.

Region Z: This region is to the left of the charges. Here, both charges are attracting each other, so there is potential for a point where the net electric field is zero. To find this point, we can set up an equation to balance the forces exerted by the charges.

The electric field due to q can be calculated using Coulomb's Law: E = k * q / r^2, where k is the Coulomb constant, q is the magnitude of charge q, and r is the distance between the charge and the point we are interested in.

Similarly, the electric field due to Q can be calculated as: E = k * Q / R^2, where Q is the magnitude of charge Q and R is the distance between the charge and the point we are interested in.

At the point where the net electric field is zero, the electric fields due to q and Q will cancel each other out. Thus, we have the equation: k * q / r^2 = k * Q / R^2.

Given that Q > q, we know that R < r for the electric fields to cancel. Therefore, the point where the net electric field is zero will be closer to charge Q than charge q.

So, in Region Z, there will be a point where the net electric field due to the two charges is zero, closer to charge Q.

To summarize:
- In Region X, it is unlikely for there to be a point where the net electric field is zero.
- In Region Y, it is unlikely for there to be a point where the net electric field is zero.
- In Region Z, there will be a point closer to charge Q where the net electric field is zero.