There are two conducting spheres of different sizes, both with the same negative charge. If they are connected with a conducting wire, the charge would therefore flow from the smaller to the larger. Am I correct? Thanks!
Let's see. You say the charge is negative. That is true, since with metal conducting spheres, it is the electrons that are free to move. The smaller sphere will have a larger negative potential (Q/r) at the surface, initially. Electrons will flow to the less negatively charged larger sphere.
Think of it this way. On the smaller sphere, the free electrons are closer together. They will repel each other and go to the larger sphere to increase the distance between them.
You are correct!
a proton is projected into a magnetic field that is directed along the positive x-axis. find the direction of the magnetic force exerted on the proton for cach of the following directions of the protons velocity
Yes, you are correct! When two conducting spheres of different sizes and same charge are connected with a conducting wire, the charge will flow from the smaller sphere to the larger sphere.
To understand why this happens, let's consider the principle of charge distribution in conductors. In a conductor, charges are free to move around due to the presence of loosely bound electrons. When two conductors are connected, they become part of the same electric system, allowing the charges to redistribute themselves until the system reaches equilibrium.
Now, let's apply this principle to your situation. Initially, the smaller sphere has a higher charge density compared to the larger sphere because it has the same amount of charge packed into a smaller surface area. This higher charge density creates a stronger electric field around the smaller sphere.
When the spheres are connected by a wire, the excess negative charge on the smaller sphere will start to distribute itself evenly across both spheres. The free electrons within the smaller sphere will repel each other and move away from one another, spreading out on the connecting wire. This redistribution of charge continues until the electric field becomes equal everywhere.
Since the larger sphere has a larger surface area, it can accommodate more charge without increasing the charge density significantly. Therefore, the smaller sphere will lose some of its excess charge as it flows towards the larger sphere, equalizing the distribution of charge. This flow of charge from the smaller sphere to the larger sphere is commonly referred to as charge transfer or charge equilibration.
In conclusion, when two conducting spheres of different sizes and the same charge are connected with a conducting wire, the charge will flow from the smaller sphere to the larger sphere until the charge distribution becomes uniform.