Just multiply out as necessary to get rid of the square roots and fractions and see what values make theta disappear,Kaguro said:
Theta is one of the two independent variables for P. The distance betwwen P and Q and P and q are functions of theta as well as r.Kaguro said:
Post 2 tells you that. Or you can cheat by googling
It's widely disseminated.haruspex said:
In fact, you'd better since the equation for Q is wrong! (Maybe typo.)Kaguro said:
Yes.Kaguro said:
Just 4 solutions?haruspex said:
Not sure what exactly your parabola equation is. R, d and q are all givens; only b and Q are outputs.Kaguro said:Just 4 solutions?
That means my parabola equation is not the only constraint?
haruspex said:
What about the terms that do not involve theta? They have to balance too.Kaguro said:
haruspex said:
The sphere image charge problem is a theoretical physics problem that involves calculating the electric potential and field around a conducting sphere in the presence of an external point charge. It is a simplified version of the more general "image charge problem" which involves calculating the electric potential and field around a conducting object in the presence of another object.
The sphere image charge problem is important because it has many practical applications in electrostatics and electromagnetism. It can be used to calculate the capacitance of a conducting sphere, which is useful in designing electrical circuits and devices. It also helps us understand the behavior of electric fields around conducting objects, which is important in many areas of physics and engineering.
The sphere image charge problem is typically solved using the method of images, which involves replacing the conducting sphere with an imaginary point charge located at a specific distance from the sphere's surface. This creates a mirror image of the original charge, and the electric potential and field can then be calculated using the superposition principle. The final solution is then adjusted to take into account the presence of the conducting sphere.
Some common assumptions made in solving the sphere image charge problem include assuming that the sphere is a perfect conductor, that the external point charge is small compared to the sphere, and that the sphere is located in a uniform electric field. These assumptions allow for a simplified solution to be obtained, but may not accurately represent real-world scenarios.
Yes, there are many real-world examples of the sphere image charge problem. For example, the Earth's ionosphere can be modeled as a conducting sphere in an external electric field, which is important in understanding the behavior of radio waves in the atmosphere. Another example is the behavior of charged particles near a metal surface, which can be modeled using the sphere image charge problem to understand phenomena such as electric discharge and surface charging.
