Exam 22: Electric Potential

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 = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C, ^mproton = 1.67 x 10^-27 kg)

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

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? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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?

A charge Q = -820 nC is uniformly distributed on a ring of 2.4 m radius. A point charge q = +530 nC 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? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x²y² + yz³ - 2z³x, 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).

The graph in the figure shows the variation of the electric potential V (measured in volts) as a function of the radial direction r (measured in meters). For which range or value of r is the magnitude of the electric field the largest?

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. An electron is released from rest at the surface of the outer conductor. What is the speed of the electron as it reaches the inner conductor? (e = 1.60 × 10^-19 C, ^mel = 9.11 x 10^-31 kg, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two large conducting parallel plates A and B are separated by 2.4 m. A uniform field of 1500 V/m, in the positive x-direction, is produced by charges on the plates. The center plane at x = 0.00 m is an equipotential surface on which V = 0. An electron is projected from x = 0.00 m, with an initial velocity of 1.0 × 10⁷ m/s perpendicular to the plates in the positive x-direction, as shown in the figure. What is the kinetic energy of the electron as it reaches plate A? (e = 1.60 × 10^-19 C, mel = 9.11 x 10^-31 kg)

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.

A -7.0-μC point charge has a positively charged object in an elliptical orbit around it. If the mass of the positively charged object is 1.0 kg and the distance varies from 5.0 mm to 20.0 mm between the charges, what is the maximum electric potential difference through which the positive object moves? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. What is the maximum electric field magnitude between the cylinders? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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 negative charge is moved from point A to point B along an equipotential surface. Which of the following statements must be true for this case?

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 nonconducting sphere contains positive charge distributed uniformly throughout its volume. 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.)

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, mproton = 1.67 x 10^-27 kg)

If the electric potential in a region is given by V(x) = 6/x², the x component of the electric field in that region is

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?