Electric Energy of Charge on Semi-Planes at Right Angle

[DiPs]

Two conducting semi-planes form a right angle. A charge q is placed between them as shown in the picture(first attachment). What is the energy of electro statical interaction of the charge with the planes?
I m confused how to approach this problem..??
Though I could think of one way(hint provided with the question) to solve it but that's not giving me the right answer..
i thought to take reflections of the charge..the reason being the following points:
The field lines should cross the conducting surface at the right angle, as any field component, parallel to the surface,would induce currents, and the surface charges would rearrange in such a way to compensate for this field component.
so if we can substitute the real system by some configuration of charges, providing the same field configuration in our region of interest, we can calculate any parameters.(second attachment)

 

[jbsteele]

After doing so I got the energy to be Kq^2/4dwhere d is the distance between two planes and k is coulomb constant..But the answer given is q^2/2ε0dCan anyone explain why am I getting wrong answer ??A:The correct answer is $\frac{q^2}{2 \epsilon_0 d}$ because this is the interaction energy of the charge $q$ with its own image charge $-q$.The hint in the problem about reflections is just a way to help you visualize what's happening, not a way to solve the problem. The image charge appears because of boundary conditions - the electric field must be normal to the surface.

 

[kerimek]

I would approach this problem by first understanding the concept of electric energy and electrostatic interactions. Electric energy is the potential energy stored in a system due to the presence of electric charges. Electrostatic interactions refer to the forces between electrically charged particles.

In this scenario, we have two conducting semi-planes forming a right angle and a charge q placed between them. To calculate the energy of electrostatic interaction, we need to consider the electric potential energy due to the presence of the charge q in the electric field created by the two semi-planes.

One way to approach this problem is by using the concept of electric potential. The electric potential at a point in an electric field is defined as the amount of work required to move a unit charge from infinity to that point. In this case, we can divide the region between the two semi-planes into smaller segments, and for each segment, we can calculate the electric potential due to the charge q. Then, by summing up all the electric potentials, we can calculate the total electric potential energy of the charge q in the electric field of the two semi-planes.

Another approach could be to use the concept of electric flux. Electric flux is defined as the number of electric field lines passing through a given area. In this case, we can calculate the electric flux due to the charge q passing through each semi-plane separately. Then, by adding the electric fluxes from both semi-planes, we can calculate the total electric flux. Finally, using the relationship between electric flux and electric potential, we can calculate the electric potential energy of the charge q in the electric field of the two semi-planes.

The approach of using reflections of the charge may not give the correct answer as it does not take into account the actual electric field created by the two semi-planes. It only considers the field lines passing through the intersection of the two semi-planes, which may not accurately represent the electric field in the region of interest.

In conclusion, as a scientist, I would approach this problem by using the concepts of electric potential and electric flux to calculate the energy of electrostatic interaction of the charge q with the two semi-planes at a right angle.