Equipotential Surfaces Practice Problems

A solid conducting sphere of radius r₁, carrying a charge -q is placed inside a hollowed conducting sphere of radius r₂ that carries a charge +q. Non-conducting supports are used to maintain this configuration of spheres. If the charge on the hollowed sphere is changed to +Q, determine if the following remains the same or will change. (Take electric potential to be zero at infinity. You may need E(r) = -∂V/∂r = (-∂/∂r)(kq/r) = kq/r².) i) Potential of solid sphere relative to hollowed sphere. ii) Electric field magnitude between the two spheres iii) Electric field outside the hollowed sphere.

A hollowed brass sphere has a radius r_b and carries a change +q. A solid aluminum ball of radius r_a carrying a charge -q is located at the center of the hollowed brass sphere. Insulating materials are used to hold the ball in place. Use E(r) = -∂V/∂r = (-∂/∂r)(kq/r) = kq/r² and the expression for electric potential outside the brass sphere to obtain an expression for the electric field outside the brass sphere.

A solid copper ball of radius r_i and carrying charge -q is placed inside a hollowed silver sphere of radius r_o and charge +q. Insulators are used to hold the copper sphere in place inside the silver sphere. Use E(r) = -∂V/∂r = (-∂/∂r)(kq/r) = kq/r² and the expression for electric potential between the two spheres (take electric potential to be zero at infinity) to derive an expression for the electric field magnitude between the two spheres. Express E(r) you derived using V_io, the potential of the copper ball relative to the silver shell.

A hollowed conducting sphere of radius r_o and charge +q is used to house a solid conducting sphere of radius r_i carrying a charge -q. Insulating supports are used to maintain the inner sphere in place. Derive an expression for V_io, the potential of the solid sphere relative to the hollowed sphere. Take electric potential to be zero at infinity.

A conducting solid sphere  (radius r_i) with charge -q is located at the center of a conducting hollowed sphere (radius r_o) with charge +q. Non-conducting supports are used to hold and maintain the solid sphere at the center of the hollowed sphere. Taking potential to be zero at r = ∞, determine the electric potential (V_r) at i) inside the solid sphere ii) between the two spheres iii) Outside the hollowed sphere. Hint: Potential at a point is the sum of potentials from each sphere.

A huge glass lamina has one of its faces charged uniformly at -5.5 nC/m². State how the electric potential varies along a line perpendicular to the lamina's surface without making calculations. Is the result dependent on chosen potential reference point?

Using the three equipotential surfaces corresponding to potentials of -150 V, 150 V, and 350 V, calculate the strength and direction of the electric field at the specific point shown as a dot in the figure below.

Consider two metallic globes. The smaller globe has a negative charge of magnitude 4.0 µC, while the larger globe, which is thrice the diameter of the first, is initially electrically neutral. A long, thin metallic strip, is then used to connect the two globes. Determine the resulting charge on each globe.

Calculate the electric field strength at the midpoint between two equipotential surfaces: one at +3.0 V and the other at -3.0 V. These surfaces are separated by a distance of 2.0 cm, and it can be assumed that the potential varies uniformly between them.

Imagine a spherical conductor with a radius of 0.45 m carrying a uniform electric charge of 0.75 μC on its surface. You are tasked with visualizing the electric field around this conductor and must draw equipotential surfaces. To get started, you want to find the radius of the first equipotential surface that is 150 V higher than the potential at the surface of the conductor. What will that radius be?