26 24. A small, charged, spherical object at the origin of a Cartesiancoordinate system contains 3.30 X 10 more electrons thanprotons. Find the magnitude and direction of the electricfield at a point that is 3 mm away from the origin.25. Two protons A and B are separated by a distanced9.00 pum. What are the magnitude and direction of theclectric field along the line connecting the protons (a) half-way between them and (b) a distance d/4 away from A and3d/4 away from B? Use the relationship between dectricforce and electric field,26. A positively charged particle initially at rest on the groundmoves 4.0 m upward in 2.00 s. If the particle has a charge-to-mass ratio of 10 µC/g and the electric field in this region isconstant and uniform, what is the magnitude and direction ofthe electric field?27. A particle, carrying a positive charge of 4 nC, located 5 cmaway from a parlicle with unknown charge q. experiences anattractive electric force of magnitude 115.2 N. (a) Determinethe value of the charge q. (b) Using the relationship betweenelectric lield and electric force and the result from part (a),determine the magnilude and direction of the dectric ielddue to the charge q al a point localed 20 cm away rom thei4nC charge in a direction orthogonal to the lune between thelwo charges28. A particle at the origin of a Cartesian coordinate system car-nes a charge ol 5.0 X 10 C What are the magnitudeand dr-rection of the elecric lield al (a(4.00 mm 0.(00N00 m),and f 3.00 m 4.00 mm29. T) Plot the valne of the radial componcat of the eltrcncdJue to a posselcharged pellet a Tunter.ot Neprthepel center h) Repeit or deller Tke Jepllet to be a ilrl ocomJuctny spiore having adiuofINS ndCaing3435.36.37. Frserthe99

Given charge mass ratio =10uC/g

moves 4.0 m upward in 2.00 s. If the particle has a charge-to- mass ratio of 10 µC/g and the electric field in this region is constant and uniform, what is the magnitude and direction of the electric field? .

moves 4.0 m upward in 2.00 s. If the particle has a charge-to- mass ratio of 10 µC/g and the electric field in this region is constant and uniform, what is the magnitude and direction of the electric field? .

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Electric Fields

Section: Chapter Questions

Problem 23.11OQ: Three charged particles are arranged on corners of a square as shown in Figure OQ23.11, with charge...

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(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in figure 18.46 is zero if the charges on the four comers are exactly equal. (b) Show that this is also true for any combination of charges in which qa= qd and qa = qc
Three charged particles are arranged on corners of a square as shown in Figure OQ23.11, with charge Q on both the particle at the upper left corner and the particle at the lower right corner and with charge +2Q on the particle at the lower left corner. (i) What is the direction of the electric field at the upper right corner, which is a point in empty space? (a) It is upward and to the right. (b) It is straight to the right. (c) It is straight downward. (d) It is downward and to the left. (e) It is perpendicular to the plane of the picture and outward. (ii) Suppose the +2Q charge at the lower left corner is removed. Then does the magnitude of the field at the upper right corner (a) become larger, (b) become smaller, (c) stay the same, or (d) change unpredictably?
(a) What is the electric field 5.00 m from die center of the terminal of a Van de Graaff with a 3.00-mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a 2.00C charge on the Van de Graaff’s belt?
A proton and an alpha particle (charge = 2e, mass = 6.64 1027 kg) are initially at rest, separated by 4.00 1015 m. (a) If they are both released simultaneously, explain why you cant find their velocities at infinity using only conservation of energy. (b) What other conservation law can be applied in this case? (c) Find the speeds of the proton and alpha particle, respectively, at infinity.
A Van de Graaff generator is charged so that a proton at its surface accelerates radially outward at 1.52 1012 m/s3. Find (a) the magnitude of the electric force on the proton at that instant and (b) the magnitude and direction of the electric field at the surface of the generator.
a point charge of magnitude 5.00 C is at the origin of a coordinate system, and a charge of 4.00 C is at the point x = 1.00 m. There is a point on the x-axis, at x less than infinity, where the electric field goes to zero. (a) Show by conceptual arguments that this point cannot be located between the charges. (b) Show by conceptual arguments that point cannot be at any location between x = 0 and negative infinity. (c) Show by conceptual arguments that the point must be between x = 1.00 m and x = positive infinity. (d) Use the values given to find the point and show that it is consistent with your conceptual argument.
A proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (c) Starting with the three-particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.
Consider n equal positively charged particles each of magnitude Q/n placed symmetrically around a circle of radius a. (a) Calculate the magnitude of the electric field at a point a distance x from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (b) Explain why this result is identical to the result of the calculation done in Example 23.8.
Why must the test charge q in the definition of the electric field be vanishingly small?
An infinite line of positive charge lies along the y axis, with charge density = 2.00 C/m. A dipole is placed with its center along the x axis at x = 25.0 cm. The dipole consists of two charges 10.0 C separated by 2.00 cm. The axis of the dipole makes an angle of 35.0 with the x axis, and the positive charge is farther from the line of charge than the negative charge. Find the net force exerted on the dipole.
A point charge of 4.00 nC is located at (0, 1.00) m. What is the x component of the electric field due to the point charge at (4.00, 2.00) m? (a) 1.15 N/C (b) 0.864 N/C (c) 1.44 N/C (d) 1.15 N/C (e) 0.864 N/C
Two particles, each with charge 52.0 nC, are located on the y axis at y = 25.0 cm and y = 25.0 cm. (a) Find the vector electric field at a point on the x axis as a function of x. (b) Find the field at x = 36.0 cm. (c) At what location is the field 1.00ikN/C? You may need a computer to solve this equation. (d) At what location is the field 16.0ikN/C?