Exam 23: Electric Potential

A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius.A point charge is fixed at the center of the ring,as shown in the figure.An electron is projected from infinity toward the ring along the axis of the ring.This electron comes to a momentary halt at a point on the axis that is 5.0 m from the center of the ring.What is the initial speed of the electron at infinity? ,k = 1/4πε₀ = ,m_el =

If the electrical potential in a region is constant,the electric field must be zero everywhere in that region.

A conducting sphere of radius R carries an excess positive charge and is very far from any other charges.Which one of the following graphs best illustrates the potential (relative to infinity)produced by this sphere as a function of the distance r from the center of the sphere?

If the potential in a region is given by V(x,y,z)= xy - 3z^-2,then the y component of the electric field in that region is

Consider the group of three+2.4 nC point charges shown in the figure.What is the electric potential energy of this system of charges relative to infinity?

When the electric field is zero at a point,the potential must also be zero there.

Two +6.0-μC point charges are placed at the corners of the base of an equilateral triangle,as shown in the figure.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)At the vertex,P,of the triangle (a)what is the electric potential (relative to infinity)due to these charges? (b)what is the magnitude of the electric field due to these charges?

Two equal point charges Q are separated by a distance d.One of the charges is released and moves away from the other due only to the electrical force between them.When the moving charge is a distance 3d from the other charge,what is its kinetic energy?

The potential as a function of position x is shown in the graph in the figure.Which statement about the electric field is true?

Two point charges of +2.0 μC and -6.0 μC are located on the x-axis at x = -1.0 cm and x = +2.0 cm respectively.Where should a third charge of +3.0-μC be placed on the +x-axis so that the potential at the origin is equal to zero? =

The figure shows an arrangement of two -4.5 nC charges,each separated by 5.0 mm from a proton.If the two negative charges are held fixed at their locations and the proton is given an initial velocity v as shown in the figure,what is the minimum initial speed v that the proton needs to totally escape from the negative charges? = , ,

A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius.A point charge is fixed at the center of the ring.Points A and B are located on the axis of the ring,as shown in the figure.What is the minimum work that an external force must do to transport an electron from B to A? ,k = 1/4πε₀ =

A very long nonconducting cylinder of diameter 10.0 cm carries charge distributed uniformly over its surface.Each meter of length carries +5.50 µC of charge.A proton is released from rest just outside the surface.How far will it be from the SURFACE of the cylinder when its speed has reached 2550 km/s? (k = 1/4πε₀ = , ,

Two parallel conducting plates are separated by and carry equal but opposite surface charge densities.If the potential difference between them is what is the magnitude of the surface charge density on each plate?

Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)

Two point charges of +1.0 μC and -2.0 μC are located 0.50 m apart.What is the minimum amount of work needed to move the charges apart to double the distance between them?

A half-ring (semicircle)of uniformly distributed charge Q has radius R.What is the electric potential at its center?

Suppose you have two negative point charges.As you move them farther and farther apart,the potential energy of this system relative to infinity

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x^2y2 + yz³ - 2z^3x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

A conducting sphere contains positive charge distributed uniformly over its surface.Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity.(There may be more than one correct choice.)