Exam 25: The Electric Potential

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? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Four point charges of magnitude 6.00 μC and of varying signs are placed at the corners of a square 2.00 m on each side,as shown in the figure.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) (a)What is the electric potential (relative to infinity)at the center of this square due to these charges? (b)What is the magnitude of the electric field due to these charges at the center of the square?

A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure.What is the potential difference,V_A - V_B,between points A and B? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two point charges,Q and -3Q,are located on the x-axis a distance d apart,with -3Q to the right of Q.Find the location of ALL the points on the x-axis (not counting infinity)at which the potential (relative to infinity)due to this pair of charges is equal to zero.

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? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two equal positive charges are held in place at a fixed distance.If you put a third positive charge midway between these two charges,its electrical potential energy of the system (relative to infinity)is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.

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?

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity).If the sphere's radius were twice as large,but the charge on the sphere were the same,what would be the potential on the surface relative to infinity?

A sphere with radius 2.0 mm carries +1.0 μC of charge distributed uniformly throughout its volume.What is the potential difference,V_B - V_A,between point B,which is 4.0 m from the center of the sphere,and point A,which is 9.0 m from the center of the sphere? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A very small object carrying -6.0 μC of charge is attracted to a large,well-anchored,positively charged object.How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is 3.0 mV? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C,m_proton = 1.67 × 10^-27 kg)

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?

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

Four equal +6.00-μC point charges are placed at the corners of a square 2.00 m on each side.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) (a)What is the electric potential (relative to infinity)due to these charges at the center of this square? (b)What is the magnitude of the electric field due to these charges at the center of the square?

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

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

Three point charges of -2.00 μC,+4.00 μC,and +6.00 μC are placed along the x-axis as shown in the figure.What is the electrical potential at point P (relative to infinity)due to these charges?

A negative charge,if free,will tend to move

A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC,and no other charges are present.(k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)The potential (relative to infinity)due to this sphere at a point 12.0 cm from its center is closest to

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