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24. Electric Force & Field; Gauss' Law

Electric Field

24. Electric Force & Field; Gauss' Law

Electric Field

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Intro to Electric Fields

Intro to Electric Fields

Electric Field due to a Point Charge

Electric Field due to a Point Charge

Zero Electric Field due to Two Charges

Zero Electric Field due to Two Charges

Electric Field Above Two Charges (Triangle)

Electric Field Above Two Charges (Triangle)

Balancing a Pendulum in Electric Field

Balancing a Pendulum in Electric Field

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Practice this topic

Multiple Choice

A 1.5μC charge, with a mass of 50g, is in the presence of an electric field that perfectly balances its gravity. What magnitude does the electric field need to be, and in what direction does it need to point?

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Multiple Choice

If two equal charges are separated by some distance, they form an electric dipole. Find the electric field at the center of an electric dipole, given by the point P in the following figure, formed by a 1C and a −1C charge separated by 1 cm.

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Multiple Choice

4 charges are arranged as shown in the following figure. Find the magnitude of the electric field at the center of the arrangement, indicated by the point P.

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Multiple Choice

In the following figure, a mass m is balanced such that its tether is perfectly horizontal. If the mass is m and the angle of the electric field is θ, what is the magnitude of the electric field, E, expressed in terms of m, q, and θ?

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Multiple Choice

1 . 2 g

plastic bead is given a charge of

- 14 nC

by rubbing. What magnitude and direction of electric field is necessary to levitate the bead?

Textbook Question

Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a. (a) Find the magnitude and direction of the electric field at x = 0.

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Textbook Question

A +8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-mC point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 * 10^8 N/C is directed parallel to the wire, as shown in Fig. E21.34.

(b) What would the tension be if both charges were negative?

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Textbook Question

A +8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-mC point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 * 10^8 N/C is directed parallel to the wire, as shown in Fig. E21.34.

(a) Find the tension in the wire.

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Textbook Question

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?

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Textbook Question

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (b) How much time does it take the proton to stop after entering the field?

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Textbook Question

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm.

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Textbook Question

A very long, straight wire has charge per unit length 3.20 * 10^-10 C/m. At what distance from the wire is the electricfield magnitude equal to 2.50 N/C?

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Textbook Question

A point charge is placed at each corner of a square with side length a. All charges have magnitude q. Two of the charges are positive and two are negative (Fig. E21.42). What is the direction of the net electric field at the center of the square due to the four charges, and what is its magnitude in terms of q and a?

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Textbook Question

a. Starting from rest, how long does it take an electron to move 1.0 cm in a steady electric field of magnitude 100 N/C?

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Textbook Question

A 10.0 nC charge is located at position (x, y)=(1.0 cm, 2.0 cm). At what (x, y) position(s) is the electric field c. (21,600 î−28,800ĵ) N/C?

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Textbook Question

A small 1.0 g block charged to 75 nC is placed on a 30° inclined plane. The coefficients of static and kinetic friction are 0.20 and 0.10, respectively. What minimum strength horizontal electric field is needed to keep the block from sliding down the plane?

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Textbook Question

An electric field E=200,000î N/C causes the point charge in FIGURE P22.68 to hang at an angle. What is θ?

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Textbook Question

A 0.10 g honeybee acquires a charge of +23 pC while flying. b. What electric field (strength and direction) would allow the bee to hang suspended in the air?

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Textbook Question

A −12 nC charge is located at (x, y)=(1.0 cm, 0 cm). What are the electric fields at the positions (x, y)=(5.0 cm, 0 cm), (−5.0 cm, 0 cm), and (0 cm, 5.0 cm)? Write each electric field vector in component form.

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Textbook Question

INT A proton is fired horizontally into a 1.0×10^5 N/C vertical electric field. It rises 1.0 cm vertically after having traveled 5.0 cm horizontally. What was the proton's initial speed?

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Textbook Question

A −15 nC charge is at x=+2.0 cm on the x-axis. A second charge q is located somewhere on the x-axis to the left of the origin. The electric field at y=2.0 cm on the y-axis is Ē =3.0×105 î N/C . What are (a) the charge q in nC and (b) its distance from the origin?

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Textbook Question

A thin, horizontal, 10-cm-diameter copper plate is charged to 3.5 nC. If the charge is uniformly distributed on the surface, what are the strength and direction of the electric field (a) 0.1 mm above the center of the top surface of the plate?

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Textbook Question

Figure 24.32b showed a conducting box inside a parallel-plate capacitor. The electric field inside the box is E (→ above E) = 0 (→ above 0) . Suppose the surface charge on the exterior of the box could be frozen. Draw a picture of the electric field inside the box after the box, with its frozen charge, is removed from the capacitor. Hint: Superposition.

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Textbook Question

The three parallel planes of charge shown in FIGURE P24.44 have surface charge densities ─ ½ η , η , and ─ ½ η. Find the electric fields EA (→ above E) to ED (→ above E) in regions A to D. The upward direction is the + y-direction.

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Textbook Question

A 0.80-μm-diameter oil droplet is observed between two parallel electrodes spaced 11 mm apart. The droplet hangs motionless if the upper electrode is 20 V more positive than the lower electrode. The density of the oil is 885 kg/m³ . (c) Does the droplet have a surplus or a deficit of electrons? How many?

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Textbook Question

CALC Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE P23.48. a. Find an expression for the electric field Ē at the center of the semicircle. Hint: A small piece of arc length Δs spans a small angle Δθ=Δs/R , where R is the radius.

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