Exam 22: Electric Charges and Forces

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

The figure shows two tiny 5.0-g spheres suspended from two very thin 1.0-m-long threads. The spheres repel each other after being charged to and hang at rest as shown. What is the angle θ? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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)

A positive point charge Q is fixed on a very large horizontal frictionless tabletop. A second positive point charge q is released from rest near the stationary charge and is free to move. Which statement best describes the motion of q after it is released?

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)

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

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, charge = 3.1 × C is placed at the origin and charge is placed on the x-axis, at x = -0.20 m. Where along the x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero?

A point charge Q is located a short distance from a point charge 3Q, and no other charges are present. If the electrical force on Q is F, what is the electrical force on 3Q?

The electric field 1.5 cm from a very small charged object points toward the object with a magnitude of 180,000 N/C. What is the charge on the object? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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 . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s² , what is the charge that it carries?

A +7.00 μC point charge and -9.00 μC point charge are placed along the x-axis at x = 0.000 cm and , 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?

In the figure, all the charges are point charges and the charge in the middle is For what charge q₁ will charge q₂ be in static equilibrium?

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

Three point charges are placed on the x-axis. A charge of +2.0 μC is placed at the origin, -2.0 μC to the right at x = 50 cm, and +4.0 μC at the 100 cm mark. What are the magnitude and direction of the electrostatic force that acts on the charge at the origin? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

The point charge at the bottom of the figure is Q = +17 nC, and the curve is a circular arc. What is the magnitude of the force on the charge Q due to the other point charges shown? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two identical small conducting spheres are separated by 0.60 m. The spheres carry different amounts of charge and each sphere experiences an attractive electric force of 10.8N. The total charge on the two spheres is -24 μC. The two spheres are now connected by a slender conducting wire, which is then removed. The electric force on each sphere is closest to

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?

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)

Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure. These spheres have equal masses of 40 g, and carry charges q₁ and q₂ of equal magnitude 2.0 μC but opposite sign. The spheres are brought into the positions shown in the figure, with a vertical separation of 15 cm between them. Note that you cannot neglect gravity. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The tension in the lower thread is closest to