(d) The charge will flow until the potential is equal on each sphere. By definition, negative charges
flow from low to high potential. So, if the potentials of the spheres are equal, no more charge will
flow.
(e) The potential at the surface of each sphere is −kQ /r , where r is the radius of the sphere. Thus, the
potential at the surface of the smaller sphere is initially more negative, and the charge will
initially flow low-to-high potential to the larger sphere.Rapid Review
• Matter is made of protons, neutrons, and electrons. Protons are positively charged, neutrons have no
charge, and electrons are negatively charged.
• Like charges repel, opposite charges attract.
• An induced charge can be created in an electrically neutral object by placing that object in an electric
field.
• Electric field lines are drawn from positive charges toward negative charges. Where an electric field
is stronger, the field lines are drawn closer together.
• The electric force on an object depends on both the object’s charge and the electric field it is in.
• Unless stated otherwise, the zero of electric potential is at infinity.
• Equipotential lines show all the points where a charged object would feel the same electric force.
They are always drawn perpendicular to electric field lines.
• The electric field between two charged parallel plates is constant. The electric field around a charged
particle depends on the distance from the particle.
• Gauss’s law says that the net electric flux through a closed surface is equal to the charge enclosed
divided by ε 0 . To solve a problem using Gauss’s law, look for planar, cylindrical, or spherical
symmetry.