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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

A Sphere in a Sphere A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net
A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly
A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is - 3Q, and it is insulated from its
Concentric Spherical Shells A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d
Repeat Problem 22.45, hut now let the outer shell have charge -2q. As in Problem 22.45, the inner shell has charge +2q.
Repeat Problem 22.45, but now let the outer shell have charge -4q. As in Problem 22.45, the inner shell has charge + 2q.
A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform
Negative charge -Q is distributed uniformly over the surface of a thin spherical insulating shell with radius R. Calculate the force (magnitude and direction) that the shell exerts on a positive
(a) How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cm in diameter to produce an electric field of 1150 N/C just outside the surface of
A single isolated, large conducting plate (Fig.) has a charge per unit area σ on its surface. Because the plate is a conductor, the electric field at its surface is perpendicular to the surface
Thomson's Model of the Atom In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In
Thomson's Model of the Atom Continued. Using Thomson's (outdated) model of the atom described in Problem 22.52, consider an atom consisting of two electrons, each of charge -e, embedded in a sphere
A Uniformly Charged Slab A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and
A Nonuniformly Charged Slab Repeat Problem 22.54, but now let the charge density of the slab be given by p(x) = P0(x/d)2, where Po is a positive constant.
Can Electric Forces Alone Give Stable Equilibrium? In Chapter 21, several examples were given of calculating the force exerted on a point charge by other point charges in its surroundings. (a)
A nonuniform, but spherically symmetric, distribution of charge has a charge density p (r) given as follows:Where P0 = 3Q/πR3 is a positive constant.(a) Show that the total charge contained in the
A nonuniform, but spherically symmetric, distribution of charge has a charge density p (r) given as follows:Where P0 is a positive constant(a) Find the total charge contained in the charge
Gauss's Law for Gravitation The gravitational force between two point masses separated by a distance r is proportional to l/r2, just like the electric force between two point charges. Because of this
Applying Gauss's Law for Gravitation Using Gauss's law for gravitation (derived in part (b) of Problem 22.59), show that the following statements are true: (a) For any spherically symmetric mass
(a) An insulating sphere with radius a has a uniform charge density p. The sphere is not centered at the origin but at r = b. Show that the electric field inside the sphere is given by E = p (r -
A very long, solid insulating cylinder with radius R has a cylindrical hole with radius a bored along its entire length. The axis of the hole is a distance b from the axis of the cylinder, where a
Positive charge Q is distributed uniformly over each of two spherical volumes with radius R. One sphere of charge is centered at the origin and the other at x = 2R (Fig. 22.44). Find the magnitude
Repeat Problem 22.63, but now let the left-hand sphere have positive charge Q and let the right-hand sphere have negative charge -Q.
Electric Field inside a Hydrogen Atom A hydrogen atom is made up of a proton of charge + Q = 1.60 X 10-19 C and an electron of charge - Q = -1.60 X 10-19 C. The proton may be regarded as a point
A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density p (r) is given byHere a is a positive constant having units of C/m3
A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density p (r} is given byHere a is a positive constant having units of C/m3.(a)
A point charge q1 = + 2.40 µC is held stationary at the origin. A second point charge q2 = -4.30 µC moves from the point x = 0.150 m, Y = 0 to the point x = 0.250 m, Y = 0.250 m. How much work is
A point charge q1 is held stationary at the origin. A second charge q2 is placed at point a, and the electric potential energy of the pair of charges is + 5.4 X 10-8 J. When the second charge is
Energy of the Nucleus How much work is needed to assemble an atomic nucleus containing three protons (such as Be) if we model it as an equilateral triangle of side 2.00 X 10-15 m with a proton at
(a) How much work would it take to push two protons very slowly from a separation of 2.00 X 10-10 m (a typical atomic distance) to 3.00 X 10-15 m (a typical nuclear distance)? (b) If the protons are
A small metal sphere, carrying a net charge of q1 = 2.80 µC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.80 µC and
How far from a -7.20-µC point charge must a +2.30-µC point charge be placed for the electric potential energy U of the pair of charges to be -0.400 J? (Take U to be zero when the charges have
A point charge Q = +4.60 µC is held fixed at the origin. A second point charge q = + 1.20 µC with mass of 2.80 X 10-4 kg is placed on the x-rods, 0.250 m from the origin. (a) What is the electric
Three equal 1.20-µC point charges are placed at the comers of an equilateral triangle whose sides are 0.500 m long. What is the potential energy of the system? (Take as zero the potential energy of
A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -3.00 nC is placed on the x-axis at x = + 20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis
Four electrons are located at the comers of a square 10.0 nm on a side, with an alpha particle at its midpoint. How much work is needed to move the alpha particle to the midpoint of one of the sides
Three point charges, which initially are infinitely far apart, are placed at the comers of an equilateral triangle with sides d. Two of the point charges are identical and have charge q. If zero net
Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 1000 km/s, measured relative to the earth. Find the maximum electrical force that these protons will exert
A uniform electric field is directed due east. Point B is 2.00 m west of point A, point C is 2.00 m east of point A and point D is 2.00 m south of A. For each point, B, C, and D, is the potential at
Identical point charges q = +5.00 µC are placed at opposite comers of a square. The length of each side of the square is 0.200 m. A point charge q0 = - 2.00 µC is placed at one of the empty comers.
A small particle has charge -5.00µC and mass 2.00 X 10-4 kg. It moves from point A, where the electric potential is VA = + 200 V, to point B, where the electric potential isVB = +500 V. The electric
A particle with a charge of +4.20 nC is in a uniform electric field E directed to the left. It is released from rest and moves to the left; after it has moved 6.00 cm, its kinetic energy is found to
A charge of 28.0 nC is placed in a uniform electric field that is directed vertically upward and has a magnitude of 4.00 X 104 V/m. What work is done by the electric force when the charge moves? (a)
Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line
A point charge has a charge of 2.50 X 10-11 C. At what distance from the point charge is the electric potential (a) 90.0 V and (b) 30.0 V? Take the potential to be zero at an infinite distance from
Two charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points
Two point charges ql = +2.40 nC and q2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.050 m from ql and 0.060 m from q2 (Fig). Take the electric potential to be zero at
Two positive point charges, each of magnitude q, are fixed on the y-axis at the points y = +a and y = -a. Take the potential to be zero at an infinite distance from the charges.(a) Show the positions
A positive charge +q is located at the point x = 0, y = -a, and a negative charge -q is located at the point x = 0, y = +a. (a) Show the positions of the charges in a diagram. (b) Derive an
Consider the arrangement of charges described in Exercise 23.23. (a) Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an
A positive charge q is fixed at the point x = 0, y = 0, and a negative charge - 2q is fixed at the point x = a, y = 0. (a) Show the positions of the charges in a diagram. (b) Derive an expression for
Consider the arrangement of point charges described in Exercise 23.25. (a) Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an
Before the advent of solid-state electronics, vacuum tubes were widely used in radios and other devices. A simple type of vacuum tube known as a diode consists essentially of two electrodes within a
At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are 4.98 V and 12.0 V/m, respectively. (Take the potential to be zero at infinity.) (a) What
A uniform electric field has magnitude E and is directed in the negative x-direction. The potential difference between point a (at x = 0.60 m) and point b (at x = 0.90 m) is 240 V. (a) which point, a
For each of the following arrangements of two point charges, find all the points along the line passing through both charges for which the electric potential V is zero (take V = 0 infinitely far from
(a)An electron is to be accelerated from 3.00 X 106 m/s to 8.00 X 106 m/s. Through what potential difference must the electron pass to accomplish this? (b)Through what potential difference must the
A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 24.0 cm. If the potential is zero at a point at infinity, find the value of the
A uniformly charged thin ring has radius 15.0 cm and total charge +24.0 nC. An electron is placed on the ring's axis a distance 30.0 cm from the center of the ring and is constrained to stay on the
An infinitely long line of charge has linear charge density 5.00 X 10-12 C/m. A proton (mass 1.67 X 10-27 kg, charge + 1.60 X 10-19 C) is 18.0 cm from the line and moving directly toward the line at
A very long wire carries a uniform linear charge density A. Using a voltmeter to measure potential difference, you find that when one probe of the meter is placed 2.50 cm from the wire and the other
A very long insulating cylinder of charge of radius 2.50 cm carries a uniform linear density of 15.0 nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other
A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.50 µC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected
A ring of diameter 8.00 cm is fixed in place and carries a charge of +5.00 µC uniformly spread over its circumference. (a) How much work does it take to move a tiny + 3.00-µC charged ball of mass
Two very large, parallel metal plates carry charge densities of the same magnitude but opposite signs (Fig). Assume they are close enough together to be treated as ideal infinite plates. Taking the
Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. (a) If the surface charge density for each plate has magnitude 47.0nC/m2, what is the
Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by 45.0 mm, and the potential difference between them is 360 V. (a) What is the magnitude of the
(a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 1.50 kV? (b) What is the potential of the sphere's
(a) Show that V for a spherical shell of radius R, that has charge q distributed uniformly over its surface, is the same as V for a solid conductor with radius R and charge q. (b) You rub an inflated
The electric field at the surface of a charged, solid, copper sphere with radius 0.200 m is 3800 N/c, directed toward the center of the sphere. What is the potential at the center of the sphere, if
A potential difference of 480 V is established between large, parallel, metal plates. Let the potential of one plate be 480 V and the other be 0 V. The plates are separated by d = 1.70 cm. (a) Sketch
A very large plastic sheet carries a uniform charge density of -6.00nC/m2 on one face. (a) As you move away from the sheet along a line perpendicular to it, does the potential increase or decrease?
In a certain region of space, the electric potential is V(x, y, z) = Axy – Bx2 + Cy, where A, B, and C are positive constants. (a) Calculate the x-, y-, and z-components of the electric field. (b)
The potential due to a point charge Q at the origin may be written as (a) Calculate E., EY' and E, using Eqs. (23.19). (b) Show that the result of part (a) agrees with Eq. (21.7) for the electric
A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal. Spherical shell with radius r b- There is charge +q on the inner sphere and charge -q on the outer
A metal sphere with radius ra = 1.20 cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius r b = 9.60 cm. Charge +q is put on the inner sphere and
A very long cylinder of radius 2.00 cm carries a uniform charge density of 1.50nC/m. (a) Describe the shape of the equipotential surfaces for this cylinder. (b) Taking the reference level for the
Figure shows the potential of a charge distribution as a function of x. Sketch a graph of the electric field E. over the region shown.
A particle with charge +7.60nC is in a uniform electric field directed to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest, it
In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume that the proton remains at rest (a) By equating the electric force to the
A vacuum tube diode (see Exercise 23.27) consists of concentric cylindrical electrodes, the negative cathode and the positive anode. Because of the accumulation of charge near the cathode, the
Two oppositely charged. Identical insulating spheres, each 50.0 cm in diameter and carrying a uniform charge of magnitude 175 µC are placed 1.00 m apart center to center (Fig).(a) If a
An Ionic Crystal Figure shows eight point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and -q, as shown. This is a model of one cell of a cubic
(a) Calculate the potential energy of a system of two small spheres, one carrying a charge of 2.00 µC and the other a charge of - 3.50 µC, with their centers separated by a distance of 0.250 m.
The H2+ Ion. The H2+ ion is composed of two protons, each of charge +e = 1.60 X 10-19 C, and an electron of charge -e and mass 9.11 X 10-31 kg. The separation between the protons is 1.07 X 10-10 m.
A small sphere with mass 1.50 g hangs by a thread between two parallel vertical plates 5.00 cm apart (Fig). The plates are insulating and have uniform surface charge densities +σ and - σ.
(a) Calculate the potential V (r} for (i) r b. Take V = 0 at r = b.(b) Show that the potential of the inner cylinder with respect to the outer is(c) Use Eq. (23.23) and the result from part (a) to
A Geiger counter detects radiation such as alpha particles by using the fact that the radiation ionizes the air along its path. A thin wire lies on the axis of a hollow metal cylinder and is
Deflection in a CRT Cathode ray tubes (CRTs) are often found in oscilloscopes and computer monitors. In Fig an electron with an initial speed of 6.50 X 106 m/s is projected along he axis midway
Deflecting Plates of an Oscilloscope the vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. Typical
Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a
A disk with radius R has uniform surface charge density σ (a) By regarding the disk as a series of thin concentric rings, calculate the electric potential V at a point on the disk's axis a
(a) From the expression for E obtained in Problem 22.40, find the expressions for the electric potential V as a function of r, both inside and outside the cylinder. Let V = 0 at the surface of the
Alpha particles (mass = 6.7 X 10-27 kg, charge = + 2e) are shot directly at a gold foil target. We can model the gold nucleus as a uniform sphere of charge and assume that the gold does not move. (a)
For the ring of charge described in Example 23.11 (Section 23.3), integrate the expression for E, found in Example 21.10 (Section 21.5) to find the potential at point P on the ring's axis. Assume
A thin insulating rod is bent into a semicircular arc of radius a, and a total electric charge Q is distributed uniformly along the rod. Calculate the potential at the center of curvature of the arc
Self-Energy of a Sphere of Charge A solid sphere of radius R contains a total charge Q distributed uniformly throughout its volume. Find the energy needed to assemble this charge by bringing
(a) From the expression for E obtained in Example 22.9 (Section 22.4), find the expression for the electric potential V as a function of r both inside and outside the uniformly charged sphere. Assume
A solid insulating sphere with radius R has charge Q uniformly distributed throughout its volume. (a) Use the results of Problem 23.72 to find the magnitude of the potential difference between the
An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of + 150.0 µC uniformly distributed over its outer surface (see Exercise 23.43). Point a is at the

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