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Exam 20: Electric Charge and Electric Field

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Question 21

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An electric dipole consists of charges ±5.00 µC separated by 1.20 mm. It is placed in a vertical electric field of magnitude 525 N/C oriented as shown in the figure. The magnitude of the net torque this field exerts on the dipole is closest to

A) 2.02 × 10^-6 N ∙ m.
B) 3.15 × 10^-6 N ∙ m.
C) 2.41 × 10^-6 N ∙ m.
D) 1.01 × 10^-6 N ∙ m.
E) 1.21 × 10^-6 N ∙ m.

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Question 22

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Two point charges of +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

A) 25.2 × 10⁶ N/C directed toward the negative charge
B) 25.2 × 10⁶ N/C directed toward the positive charge
C) 25.2 × 10⁵ N/C directed toward the negative charge
D) 25.2 × 10⁵ N/C directed toward the positive charge
E) 25.2 × 10⁴ N/C directed toward the negative charge

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Question 23

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In the figure, a proton is projected horizontally midway between two parallel plates that are separated by 0.50 cm. The electrical field due to the plates has magnitude 610,000 N/C between the plates away from the edges. If the plates are 5.60 cm 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, mel = 9.11 × 10^-31 kg)

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)

An electric field is set up between two parallel plates, each of area 2.0 m², by putting 1.0 μC of charge on one plate and -1.0 μC of charge on the other. The plates are separated by 4.0 mm with their centers opposite each other, and the charges are distributed uniformly over the surface of the plates. What is the magnitude of the electric field between the plates at a distance of 1.0 mm from the positive plate, but not near the edges of the plates? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Two thin 80.0-cm rods are oriented at right angles to each other. Each rod has one end at the origin of the coordinates, and one of them extends along the +x-axis while the other extends along the +y-axis. The rod along the +x-axis carries a charge of -15.0 µC distributed uniformly along its length, and the other rod carries +15.0 µC uniformly over its length. Find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm, 40.0 cm). (e = 1.60 × 10^-19 C, ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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

In the figure Q = 5.8 nC and all other quantities are accurate to 2 significant figures. What is the magnitude of the force on the charge Q? (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

A dipole with a positive charge of 2.0 μC and a negative charge of -2.0 μC is centered at the origin and oriented along the x-axis with the positive charge located to the right of the origin. The charge separation is 0.0010 m. Find the electric field due to this dipole at the point x = 4.0 m, y = 0.0 m. (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²)

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)

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?

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

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)

Two point charges, Q₁ = -1.0 μC and Q₂ = + 4.0 μC, are placed as shown in the figure. (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²) The y component of the electric field, at the origin O, is closest to

A very long wire carries a uniform linear charge density of 7.0 nC/m. What is the electric field strength 16.0 m from the center of the wire at a point on the wire's perpendicular bisector? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

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 electric field strength in the space between two closely spaced parallel disks is 1.0 × 10⁵ N/C. This field is the result of transferring 3.9 × 10⁹ electrons from one disk to the other. What is the diameter of the disks? (e = 1.60 × 10^-19 C, ε0 = 8.85 × 10^-12 C²/N ∙ m²)

In the figure, a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it. A point charge Q is placed at the center of the ring. The electric field is equal to zero at field point P, which is on the axis of the ring, and 0.73 m from its center. (ε0 = 8.85 × 10^-12 C²/N ∙ m²) The point charge Q is closest to

What is the minimum magnitude of an electric field that balances the weight of a plastic sphere of mass 6.4 g that has been charged to -3.0 nC?

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)