Exam 19: The First Law of Thermodynamics

Potential due to point-charges: 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?

Spheres of charge: 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)

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

Potential energy of point-charges: 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)

Spheres of charge: 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.)

Lines of charge: 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)

Electric field and potential : 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?

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

Spheres of charge: 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

Potential energy of point-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?

Lines of charge: An extremely long thin wire carries a uniform linear charge density of 358 nC/m. Find the potential difference between points 5.0 m and 6.0 m from the wire, provided they are not near either end of the wire. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Electric field and potential : The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units). Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis?

Potential energy of point-charges: 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

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

Charged ring: 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)

Equipotential surfaces: 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?

Parallel plates: 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, m_el = 9.11 × 10^-31 kg)

Potential due to point-charges: 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.

Lines of charge: 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, m_proton = 1.67 × 10^-27 kg)

Spheres of charge: A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity). Which of the following plots correctly shows the potential as a function of distance from the center of the sphere?