Exam 17: Temperature and Heat

Parallel plates: Two very large, flat plates are parallel to each other. Plate A, located at y = 1.0 cm, is along the xz-plane and carries a uniform surface charge density -1.00 μC/m². Plate B is located at y = -1.0 cm and carries a uniform surface charge density +2.00 μC/m². What is the electric field vector at the point having x, y, z coordinates (-0.50 cm, 0.00 cm, 0.00 cm)? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Coulomb's law: A 1.0-C point charge is 15 m from a second point charge, and the electric force on one of them due to the other is 1.0 N. What is the magnitude of the second charge? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Electric field of multiple point-charges: Two point charges Q₁ and Q₂ of equal magnitudes and opposite signs are positioned as shown in the figure. Which of the arrows best represents the net electric field at point P due to these two charges?

Electric field of a single point-charge: An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of 1.0 m from the center of the nucleus? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19C)

Coulomb's law: Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

Parallel plates: Two flat 4.0 cm × 4.0 cm electrodes carrying equal but opposite charges are spaced 2.0 mm apart with their midpoints opposite each other. Between the electrodes but not near their edges, the electric field strength is 2.5 × 10⁶ N/C. What is the magnitude of the charge on each electrode? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Charge in an electric field: A point charge Q of mass 8.50 g hangs from the horizontal ceiling by a light 25.0-cm thread. When a horizontal electric field of magnitude 1750 N/C is turned on, the charge hangs away from the vertical as shown in the figure. The magnitude of Q is closest to

Parallel plates: Two very large parallel sheets a distance d apart have their centers directly opposite each other. The sheets carry equal but opposite uniform surface charge densities. A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets. If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet, what force will feel?

Infinite line of charge: At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Motion of a charged particle: An electron is initially moving to the right when it enters a uniform electric field directed upwards. Which trajectory shown below will the electron follow?

Electric field of multiple point-charges: The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to these two charges is zero?

Motion of a charged particle: In the figure, a proton is projected horizontally midway between two parallel plates that are separated by The electrical field due to the plates has magnitude between the plates away from the edges. If the plates are long, find the minimum speed of the proton if it just misses the lower plate as it emerges from the field. (e = 1.60 × 10^-19 C, ε₀ = 8.85 × 10^-12 C²/N ∙ m², m_el = 9.11 × 10^-31 kg)

Multiple point-charges: Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Coulomb's law: Charge Q₁ = 6.0 nC is at (0.30 m, 0), charge Q₂ = -1.0 nC is at (0, 0.10 m), and charge Q₃ = 5.0 nC is at (0, 0). What are the magnitude and direction of the net electrostatic force on the 5.0-nC charge due to the other charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Infinite line of charge: A long, thin rod parallel to the y-axis is located at x = -1.0 cm and carries a uniform linear charge density of +1.0 nC/m. A second long, thin rod parallel to the z-axis is located at x = +1.0 cm and carries a uniform linear charge density of -1.0 nC/m. What is the net electric field due to these rods at the origin? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Electric field of multiple point-charges: Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure. Which of the arrows represents the direction of the net electric field at the center of the square?

Electric field of a single point-charge: A small glass bead has been charged to 8.0 nC. What is the magnitude of the electric field 2.0 cm from the center of the bead? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Multiple point-charges: A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Coulomb's law: One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the distance between the balls in the test tube would become

Coulomb's law: A + 7.00 μC point charge and - 9.00 μC point charge are placed along the x-axis at x = 0.000 cm and x = 40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net electric force due to the other two charges?