Exam 20: Electric Charge and Electric Field

A metal sphere of radius 10 cm carries a charge of +2.0 μC uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere's surface? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

In the figure, all the charges are point charges and the charge in the middle is Q = -3.1 nC. For what charge q₁ will charge q₂ be in static equilibrium?

In the figure, a small spherical insulator of mass 6.00 × 10^-2 kg and charge +0.400 μC is hung by a thin wire of negligible mass. A charge of -0.220 μC is held 0.290 m away from the sphere and directly to the right of it, so the wire makes an angle θ with the vertical, as shown. What is the angle θ? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of vo = 2.0 × 10⁷ m/s, as shown in the figure. (e = 1.60 × 10^-19 C, ε0 = 8.85 × 10^-12 C²/N ∙ m², mel = 9.11 × 10^-31 kg) The velocity of the electron as it strikes plate B is closest to

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?

When two point charges are 2.0 cm apart, each one experiences a 1.0-N electric force due to the other charge. If they are moved to a new separation of 8.0 cm, the electric force on each of them is closest to

A 3.0-μC positive point charge is located at the origin and a 2.0-μC positive point charge is located at x = 0.00 m, y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.

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)

Two large, flat, horizontally oriented plates are parallel to each other, a distance d apart. Half way between the two plates the electric field has magnitude E. If the separation of the plates is reduced to d/2 what is the magnitude of the electric field half way between the plates?

A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10^-19C)

An electric dipole is made of two charges of equal magnitudes and opposite signs. The positive charge, q = 1.0 μC, is located at the point (x, y, z) = (0.00 cm, 1.0 cm, 0.00 cm), while the negative charge is located at the point (x, y, z) = (0.00 cm, -1.0 cm, 0.00 cm). How much work will be done by an electric field = (3.0 × 106 N/C) î to bring the dipole to its stable equilibrium position?

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

A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of v0 = 1.0 × 10⁷ m/s, as shown in the figure. (e = 1.60 × 10^-19 C, ε0 = 8.85 × 10^-12 C²/N ∙ m², mel = 9.11 × 10^-31 kg) The distance of closest approach of the electron to plate B is nearest to

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?

A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C î. If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s² î, what is the charge that it carries?

A point charge Q = -500 nC and two unknown point charges, q₁ and q₂, are placed as shown in the figure. The electric field at the origin O, due to charges Q, q₁ and q₂, is equal to zero. The charge q₁ is closest to

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)

X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure (a). Sphere Y is now moved away from X, as in Figure (b). What are the final charge states of X and Y?