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Exam 23: The Electric Field

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Question 21

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A thin, circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin. The disk carries a total charge of +3.00 μC distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x = 15.0 cm along the x-axis. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A) 9.95 × 10⁵ N/C
B) 4.98 × 10⁵ N/C
C) 3.31 × 10⁵ N/C
D) 2.49 × 10⁵ N/C
E) 1.99 × 10⁵ N/C

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Question 22

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A dipole with a positive charge of and a negative charge of 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 (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A) 0.56 N/C
B) -0.56 N/C
C) 0.28 N/C
D) -0.28 N/C

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Question 23

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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)

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?

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)

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)

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 v_o = 1.0 × 10⁷ m/s, as shown in the figure. (e = 1.60 × 10^-19 C, ε₀ = 8.85 × 10^-12 C²/N ∙ m², m_el = 9.11 × 10^-31 kg) The distance of closest approach of the electron to plate B is nearest to

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)

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

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) to bring the dipole to its stable equilibrium position?

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

The electric field strength in the space between two closely spaced parallel disks is .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)