# With the help of a given charge is it possible to obtain a charge many times greater in magnitude

Consider a spherically conducting sphere. If a charge(say positive) is placed near the sphere, then it will lead to separation of charges inside the sphere.My question is, can we create charges more than the magnitude of charge being used by us?

Bring your unit positive inducing charge very near the sphere. This will polarize the sphere with negative charge density nearest the inducing charge and positive charge on the far side. You can compute the exact density by finding the image charges, writing down the equation for V outside thes sphere, and finding $\partial V \over \partial N$ on the surface. Now carefully cut the sphere along the circular path which seperates the positively and negatively charged portions of the sphere. Move the positively charged portion far away from the system. It maintains its total charge of +1 (assuming your inducing charge was very near the sphere when you cut it). Now bring the negatively charged remaining part of the sphere close to the test charge. That partial shell will (again!) be polarized, with part of the far parts of surface being positively charged, but the closest part towards the unit inducing charge being negative. (you have to bring them close enough together to insure enough charge seperation.) Again, cut the shell along the contour seperating the positive and negative parts and move the positive portion far away. The remaining part of the shell has a net negative charge of more than unity. The (two) positive parts of the shell you moved away have a net positive charge of more than unity combined.