Exam 25: The Electric Potential

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?

If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.

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

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

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)

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.

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?

The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly. What is the value of the electric potential at the center of the circle?

A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius. A point charge q = +480 nC 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? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², m_el = 9.11 × 10^-31 kg )

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?

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 tiny object carrying a charge of +3.00 μC and a second tiny charged object are initially very far apart. If it takes of work to bring them to a final configuration in which the object i is at x = 1.00 mm, y = 1.00 mm, and the other charged object is at x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge on the second object. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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

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)

Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) (a) What is the potential at point A (relative to infinity) due to these charges? (b) What is the potential at point B (relative to infinity) due to these charges?

If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², ^m_el = 9.11 × 10^-31 kg)

If the electric potential at a point in space is zero, then the electric field at that point must also be zero.

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

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? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A negative charge, if free, will tend to move