An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly...

All examples of Gausss law have used highly symmetric surfaces where the flux integral is either zero or EA. Yet weve claimed that the net Φ e = Q in /Ñ 0 is independent of the...

An electron moves along the trajectory of FIGURE Q25.3 from i to f. a. Does the electric potential energy increase, decrease, or stay the same? Explain.b. Is the electron??s speed at f greater than,...

A sphere of radius R has total charge Q. The volume charge density (C/m 3 ) within the sphere is (r) = C/r 2 , where C is a constant to be determined. a. The charge within a small volume dV is dq = ...

A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. The experiment is repeated with...

FIGURE Q25.9 shows two points inside a capacitor. Let V = 0 V at the negative plate.a. What is the ratio V 2 /V 1 of the electric potentials? Explain.b. What is the ratio E 2 /E 1 of the electric...

Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero. | FIGURE Q25.12

What potential difference is needed to accelerate an electron from rest to a speed of 2.0 10 6 m/s?

A proton with an initial speed of 800,000 m/s is brought to rest by an electric field. a. Did the proton move into a region of higher potential or lower potential? b. What was the potential...

FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials V a to V c . a. b. +, +)...

Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100 m in vacuum?

Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0 10 5 V/m. a. What is the voltage across the capacitor? b. An electron is...

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. a. What is the electric potential of the proton at the position of the electron? b. What is...

What is the electric potential at the point indicated with the dot in FIGURE EX25.31? 1.0 nC 3.0 cm,' 3.0 cm 3.0 cm -2.0 nC -2.0 nC FIGURE EX25.31

The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot? ++++++++ FIGURE EX25.35

A proton moves along the x-axis where some arrangement of charges has produced the potential V(x) = V 0 sin(2x/, where V 0 = 5000 V and = 1.0 mm. a. What minimum speed must the proton have at x = 0...

Two 2.0 g plastic buttons each with +50 nC of charge are placed on a frictionless surface 2.0 cm (measured between centers) on either side of a 5.0 g button charged to +250 nC. All three are released...

What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10 nC?

Three electrons form an equilateral triangle 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?

Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do so, youre going to use a spring with spring constant 0.65...

A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. What initial speed does the proton need to just reach the...

A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm. If the proton is fired at a speed of 4.0 10 7 m/s,...

In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons,...

Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is...

A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. a. How...

Two positive point charges q are located on the y-axis at y = 1/2s. a. Find an expression for the potential along the x-axis. b. Draw a graph of V versus x for - < x < . For comparison, use a...

The wire in FIGURE P25.73 has linear charge density λ. What is the electric potential at the center of the semicircle? 2R 2R FIGURE P25.73

You are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem. (1.67 X 10-27...

A thin rod of length L and total charge Q has the nonuniform linear charge distribution (x) = 0 x/L, where x is measured from the rods left end. a. What is 0 in terms of Q and L? b. What is the...

A 1.0-m-diameter oil droplet (density 900 kg/m 3 ) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0 mm from a very wide plane of positive charge, after...

A point charge Q is distance r from a dipole consisting of charges q separated by distance s. The dipole is initially oriented so that Q is in the plane bisecting the dipole. Immediately after the...

Both batteries in Figure Q27.8 are ideal and identical, and all lightbulbs are the same. Rank in order, from brightest to least bright, the brightness of bulbs a to c. Explain. 00 Q00 000 FIGURE Q27.8

The wires leading to and from a 0.12-mm-diameter lightbulb filament are 1.5 mm in diameter. The wire to the filament carries a current with a current density of 4.5 10 5 A/m 2 . What are (a) The...

The current in a wire is doubled. What happens to (a) The current density, (b) The conduction-electron density, (c) The mean time between collisions, (d) The electron drift speed? Are each of these...

A car battery is rated at 90 A h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much...

What is the mean time between collisions for electrons in (a) An aluminum wire (b) An iron wire?

What is the resistance of a. A 2.0-m-long gold wire that is 0.20 mm in diameter? b. A 10-cm-long piece of carbon with a 1.0 mm 1.0 mm square cross section?

The electric field inside a 30-cm-long copper wire is 5.0 mV/m. What is the potential difference between the ends of the wire?

a. How long must a 0.60-mm-diameter aluminum wire be to have a 0.50 A current when connected to the terminals of a 1.5 V flashlight battery? b. What is the current if the wire is half this length?

A circuit calls for a 0.50-mm-diameter copper wire to be stretched between two points. You dont have any copper wire, but you do have aluminum wire in a wide variety of diameters. What diameter...

Household wiring often uses 2.0-mm-diameter copper wires. The wires can get rather long as they snake through the walls from the fuse box to the farthest corners of your house. What is the potential...

The electron beam inside an old television picture tube is 0.40 mm in diameter and carries a current of 50 A . This electron beam impinges on the inside of the picture tube screen. a. How many...

Energetic particles, such as protons, can be detected with a silicon detector. When a particle strikes a thin piece of silicon, it creates a large number of free electrons by ionizing silicon atoms....

Figure P27.42 shows a 4.0-cm-wide plastic film being wrapped onto a 2.0-cm-diameter roller that turns at 90 rpm. The plastic has a uniform surface charge density of -2.0 nC/cm 2 . a. What is the...

Youve been asked to determine whether a new material your company has made is ohmic and, if so, to measure its electrical conductivity. Taking a 0.50 mm 1.0 mm 45 mm sample, you wire the ends of...

The starter motor of a car engine draws a current of 150 A from the battery. The copper wire to the motor is 5.0 mm in diameter and 1.2 m long. The starter motor runs for 0.80 s until the car engine...

The resistivity of a metal increases slightly with increased temperature. This can be expressed as = 0 [ 1 + (T - T 0 )], where T 0 is a reference temperature, usually 20C, and is the temperature...

The resistivity of a metal increases slightly with increased temperature. This can be expressed as = 0 [1 + (T - T 0 )], where T 0 is a reference temperature, usually 20C, and is the temperature...

You need to design a 1.0 A fuse that blows if the current exceeds 1.0 A. The fuse material in your stockroom melts at a current density of 500 A/cm 2 . What diameter wire of this material will do the...

The current supplied by a battery slowly decreases as the battery runs down. Suppose that the current as a function of time is I = (0.75 A)e -t/(6 h) . What is the total number of electrons...

An aluminum wire consists of the three segments shown in FIGURE P27.64. The current in the top segment is 10 A. For each of these three segments, find the a. Current I. b. Current density J. c....

The batteries in Figure P27.68 are identical. Both resistors have equal currents. What is the resistance of the resistor on the right? R ? FIGURE P27.68 3.

Figure CP27.74 shows a wire that is made of two equaldiameter segments with conductivities Ï 1 and Ï 2 . When current I passes through the wire, a thin layer of charge appears at the...

Rank in order, from largest to smallest, the currents I a to I d through the four resistors in FIGURE Q28.1. + 2V - + 1V - 2 + 2V - 1 + 1V - 1 Ia FIGURE Q28.1

The switch in Figure 28.38a closes at t = 0 s and, after a very long time, the capacitor is fully charged. Find expressions for Figure 28.38a (a) The total energy supplied by the battery as the...

A 150 F defibrillator capacitor is charged to 1500 V. When fired through a patients chest, it loses 95% of its charge in 40 ms. What is the resistance of the patients chest?

A circuit you're building needs an ammeter that goes from 0 mA to a full-scale reading of 50 mA. Unfortunately, the only ammeter in the storeroom goes from 0A to a full scale reading of only 500A....

Suppose you have resistors 2.5 k, 3.5 k, and 4.5 k and a 100 V power supply. What is the ratio of the total power delivered to the resistors if they are connected in parallel to the total power...

For an ideal battery (r = 0 ), closing the switch in FIGURE P28.54 does not affect the brightness of bulb A. In practice, bulb A dims just a little when the switch closes. To see why, assume that the...

What is the time constant for the discharge of the capacitors in FIGURE EX28.34? 2 F 1 kn kn 2 F FIGURE EX28.34

What is the equivalent resistance between points a and b in FIGURE EX28.27? 100 100 ww 100 n WW ww- ww 100 0 b -ww a 100 N Lww 100 N ww FIGURE EX28.27

What is the equivalent resistance between points a and b in FIGURE EX28.26? 10 55 40 N 200 10 FIGURE EX28.26 ww

Two of the three resistors in FIGURE EX28.22 are unknown but equal. The total resistance between points a and b is 75 . What is the value of R? R ww- 200 ww a R ww FIGURE EX28.22

Compared to an ideal battery, by what percentage does the battery??s internal resistance reduce the potential difference across the 20 resistor in FIGURE EX28.20? 10 N 10 15 V 20 FIGURE EX28.20

The voltage across the terminals of a 9.0 V battery is 8.5 V when the battery is connected to a 20 load. What is the batterys internal resistance?

The circuit in FIGURE EX28.18 is called a voltage divider.What value of R will make V out = V in /10? ER Va 100 n V FIGURE EX28.18

What is the value of resistor R in FIGURE EX28.16? AV = 5.0 V 10 0 150 R ww www- FIGURE EX28.16 I= 100 mA

Bulbs A and B in FIGURE Q28.12 are identical, and both are glowing. What happens to each bulb when the switch is closed? Does its brightness increase, stay the same, decrease, or go out? Explain....

Bulbs A and B in FIGURE Q28.11 are identical, and both are glowing. Bulb B is removed from its socket. Does the potential difference ÎV 12 between points 1 and 2 increase, stay the same,...

Initially bulbs A and B in FIGURE Q28.9 are glowing. What happens to each bulb if the switch is closed? Does it get brighter, stay the same, get dimmer, or go out? Explain. A B FIGURE Q28.9

a. What are the magnitude and direction of the current in the 18 resistor in FIGURE EX28.5? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling cw...

The circuit of FIGURE Q28.5 has two resistors, with R 1 > R 2 . Which of the two resistors dissipates the larger amount of power? Explain. R2 R1 FIGURE Q28.5 ww-

In FIGURE EX28.3, what is the magnitude of the current in the wire to the right of the junction? Does the charge in this wire flow to the right or to the left? 4 V - 1 20 5015 V FIGURE EX28.3

The wire is broken on the right side of the circuit in FIGURE Q28.3. What is the potential difference V 1 - V 2 between points 1 and 2? Explain. 1 3 V. 2 FIGURE Q28.3

What is the magnitude of the potential difference across each resistor in FIGURE EX28.6? 40 N 50 V 60 N ww FIGURE EX28.6

For what emf E does the 200 resistor in FIGURE P28.64 dissipate no power? Should the emf be oriented with its positive terminal at the top or at the bottom? 100 0 300 N 50 V :200 N E? FIGURE P28.64

Electrons flow through a 1.6-mm-diameter aluminum wire at 2.0 10 -4 m/s. How many electrons move through a cross section of the wire each day?

An aeration basin is filled to a volume of 425 m 3 with wastewater containing dissolved hydrogen sulfide (H 2 S) of initial concentration 0.300 gmole/m 3 . The aeration basin is equipped with 10 gas...

A waste gas of total inlet flow rate 10.0 lbmole/ft 2 · h containing 0.050 moles solute A/mole carrier gas is treated counter currently in packed tower with a nonvolatile, solute- free...

The 2.728-K blackbody radiation has its peak wavelength at 1.062 mm. What was the peak wavelength at t = 700,000 y when the temperature was 3000 K?

An aqueous waste stream containing 1.0 mole% of hydrogen sulfide (H 2 S) dissolved in water will be treated by stripping the liquid with air in a counter current packed tower at 20C and 12.50 atm...

It is desired to remove 83.3% of dissolved NH 3 from an aqueous stream containing 10.7 mole% NH 3 in water using a packed tower in counter current flow at 1.0 atm and 30°C. The flow rate of this...

A neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie?

Exit gas from an amination reactor contains 10 mole% ammonia (NH 3 ) vapor in a nitrogen (N 2 ) carrier gas. This gas mixture is fed into the bottom of a packed tower at a molar flow rate of 2.0...

What is the current direction in the wire of FIGURE Q29.5? Explain. FIGURE Q29.5 x x x x

What is the initial direction of deflection for the charged particles entering the magnetic fields shown in FIGURE Q29.7? a. b.

A biophysics experiment uses a very sensitive magnetic field probe to determine the current associated with a nerve impulse traveling along an axon. If the peak field strength 1.0 mm from an axon is...

The south pole of a bar magnet is brought toward the current loop of FIGURE Q29.11. Does the bar magnet attract, repel, or have no effect on the loop? Explain. FIGURE Q29.11 %24

What is the line integral of B between points i and f in FIGURE EX29.24? 1.0 cm -Integration path 2.0 A 6.0 cm FIGURE EX29.24

A proton moves in the magnetic field B = 0.50 i T with a speed of 1.0 10 7 m/s in the directions shown in FIGURE EX29.26. For each, what is magnetic force F on the proton? Give your answers in...

To five significant figures, what are the cyclotron frequencies in a 3.0000 T magnetic field of the ions (a) O 2 + , (b) N 2 + , (c) CO + ? The atomic masses are shown in the table; the mass of the...

What is the net force (magnitude and direction) on each wire in FIGURE EX29.36? 10 A 2.0 cm 10 A 2.0 cm 10 A 50 cm FIGURE EX29.36 2.

A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x = -2.0 cm. A second, parallel wire carrying a 3.0 A current intersects the x-axis at x = +2.0 cm. At what...

The two insulated wires in FIGURE P29.42 cross at a 30° angle but do not make electrical contact. Each wire carries a 5.0 A current. Points 1 and 2 are each 4.0 cm from the intersection and...

Find an expression for the magnetic field strength at the center (point P) of the circular arc in FIGURE P29.45. `R FIGURE P29.45

A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 6.5-m-long, 2.0-mm diameter wire of the...

Weak magnetic fields can be measured at the surface of the brain. Although the currents causing these fields are quite complicated, we can estimate their size by modeling them as a current loop...

The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart. a. It is estimated that...

a. A 65-cm-diameter cyclotron uses a 500 V oscillating potential difference between the dees. What is the maximum kinetic energy of a proton if the magnetic field strength is 0.75 T? b. How many...

The uniform 30 mT magnetic field in FIGURE P29.65 points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.0 Ã 10 6 m/s and at an angle of 30°...