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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

Equation 30.26 is an expression for the induced electric field inside a solenoid (r < R). Find an expression for the induced electric field outside a solenoid (r > R) in which the magnetic
The magnetic field at one place on the earth’s surface is 55 μT in strength and tilted 60° down from horizontal. A 200-turn coil having a diameter of 4.0 cm and a resistance of 2.0 Ω is
A 10-turn coil of wire having a diameter of 1.0 cm and a resistance of 0.20 Ω is in a 1.0 mT magnetic field, with the coil oriented for maximum flux. The coil is connected to an uncharged 1.0 μF
Experiments to study vision often need to track the movements of a subject??s eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses with a coil
FIGURE P30.59 shows a U-shaped conducting rail that is oriented vertically in a horizontal magnetic field. The rail has no electric resistance and does not move. A slide wire with mass m and
You??ve decided to make the magnetic projectile launcher shown in FIGURE P30.58 for your science project. An aluminum bar of length l slides along metal rails through a magnetic field B. The switch
The 10-cm-wide, zero-resistance slide wire shown in FIGURE P30.57 is pushed toward the 2.0 Ω resistor at a steady speed of 0.50 m/s. The magnetic field strength is 0.50 T. a. How big is the pushing
Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a 0.20 T field
A 20-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure 30.26.) On the opposite side, a 1.0 Î©
The L-shaped conductor in FIGURE P30.54 moves at 10 m/s across and touches a stationary L-shaped conductor in a 0.10 T magnetic field. The two vertices overlap, so that the enclosed area is zero, at
The square loop shown in FIGURE P30.53 moves into a 0.80 T magnetic field at a constant speed of 10 m/s. The loop has a resistance of 0.10 Ω, and it enters the field at t = 0 s. a. Find the induced
A rectangular metal loop with 0.050 Ω resistance is placed next to one wire of the RC circuit shown in FIGURE P30.52. The capacitor is charged to 20 V with the polarity shown, then the switch is
A small, 2.0-mm-diameter circular loop with R = 0.020 Ω is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from +1.0 A
A 40-turn, 4.0-cm-diameter coil with R = 0.40 Ω surrounds a 3.0-cm-diameter solenoid. The solenoid is 20 cm long and has 200 turns. The 60 Hz current through the solenoid is I = I0 sin(2πft). What
An electric generator has an 18-cm-diameter, 120-turn coil that rotates at 60 Hz in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to
FIGURE P30.48 shows two 20-turn coils tightly wrapped on the same 2.0-cm-diameter cylinder with 1.0-mm-diameter wire. The current through coil 1 is shown in the graph. Determine the current in coil 2
FIGURE P30.47 shows a 1.0-cm-diameter loop with R = 0.50 Ω inside a 2.0-cm-diameter solenoid. The solenoid is 8.0 cm long, has 120 turns, and carries the current shown in the graph. A positive
FIGURE P30.46 shows a 4.0-cm-diameter loop with resistance 0.10 Ω around a 2.0-cm-diameter solenoid. The solenoid is 10 cm long, has 100 turns, and carries the current shown in the graph. A positive
A 2.0 cm × 2.0 cm square loop of wire with resistance 0.010 Ω has one edge parallel to a long straight wire. The near edge of the loop is 1.0 cm from the wire. The current in the wire is increasing
A 20 cm × 20 cm square loop of wire lies in the xy-plane with its bottom edge on the x-axis. The resistance of the loop is 0.50 Ω. A magnetic field parallel to the z-axis is given by B = 0.80y2t,
A 3.0-cm-diameter, 10-turn coil of wire, located at z = 0 in the xy-plane, carries a current of 2.5 A. A 2.0-mm-diameter conducting loop with 2.0 × 10-4 Ω resistance is also in the xy-plane at the
A spherical balloon with a volume of 2.5 L is in a 45 mT uniform, vertical magnetic field. A horizontal elastic but conducting wire with 2.5 Ω resistance circles the balloon at its equator. Suddenly
A circular loop made from a flexible, conducting wire is shrinking. Its radius as a function of time is r = r0e-βt. The loop is perpendicular to a steady, uniform magnetic field B. Find an
A 100-turn, 8.0-cm-diameter coil is made of 0.50-mm diameter copper wire. A magnetic field is parallel to the axis of the coil. At what rate must B increase to induce a 2.0 A current in the coil?
A 100-turn, 2.0-cm-diameter coil is at rest with its axis vertical. A uniform magnetic field 60° away from vertical increases from 0.50 T to 1.50 T in 0.60 s. What is the induced emf in the coil?
A 20 cm × 20 cm square loop has a resistance of 0.10 Ω. A magnetic field perpendicular to the loop is B = 4t - 2t2, where B is in tesla and t is in seconds. What is the current in the loop at t =
The switch in FIGURE EX30.36 has been open for a long time. It is closed at t = 0 s. a. What is the current through the battery immediately after the switch is closed?b. What is the current through
At t = 0 s, the current in the circuit in FIGURE EX30.35 is I0. At what time is the current 1/2 I0? 200 1 ww 75 mH ww- 100 N FIGURE EX30.35 lell
What value of resistor R gives the circuit in FIGURE EX30.34 a time constant of 25 μs? 500 N ww ww R 17.5 mH FIGURE EX30.34
The switch in FIGURE EX30.33 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. a. What is the maximum current through the inductor?b. What is the first time at which the
An LC circuit has a 10 mH inductor. The current has its maximum value of 0.60 A at t = 0 s. A short time later the capacitor reaches its maximum potential difference of 60 V. What is the value of the
An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15 mH coil. To what value should the capacitance be set to detect a 450 MHz
A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?
An FM radio station broadcasts at a frequency of 100 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station?
MRI (magnetic resonance imaging) is a medical technique that produces detailed “pictures” of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.0 m
How much energy is stored in a 3.0-cm-diameter, 12-cm long solenoid that has 200 turns of wire and carries a current of 0.80 A?
A 100 mH inductor whose windings have a resistance of 4.0 Ω is connected across a 12 V battery having an internal resistance of 2.0 Ω. How much energy is stored in the inductor?
What is the potential difference across a 10 mH inductor if the current through the inductor drops from 150 mA to 50 mA in 10 μs?What is the direction of this potential difference? That is, does the
The maximum allowable potential difference across a 200 mH inductor is 400 V. You need to raise the current through the inductor from 1.0 A to 3.0 A. What is the minimum time you should allow for
The charger for your electronic devices is a transformer.Suppose a 60 Hz outlet voltage of 120 V needs to be reduced to a device voltage of 3.0 V. The side of the transformer attached to the
Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down
Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength 1.5 m from the center of
The magnetic field inside a 5.0-cm-diameter solenoid is 2.0 T and decreasing at 4.0 T/s. What is the electric field strength inside the solenoid at a point(a) On the axis(b) 2.0 cm from the axis?
The magnetic field in FIGURE EX30.19 is decreasing at the rate 0.10 T/s. What is the acceleration (magnitude and direction) of a proton initially at rest at points a to d? 2.0 сm b d a Tem"1 cm"I
A 1000-turn coil of wire 1.0 cm in diameter is in a magnetic field that increases from 0.10 T to 0.30 T in 10 ms. The axis of the coil is parallel to the field. What is the emf of the coil?
The resistance of the loop in FIGURE EX30.15 is 0.20 Ω. Is the magnetic field strength increasing or decreasing? At what rate (T/s)? 150 mA x x x X x x X 8.0 сm x x X x x x X 8.0 сm
For the circuit of FIGURE Q30.14: a. What is the battery current immediately after the switch closes? Explain.b. What is the battery current after the switch has been closed a long time? Explain. 50
FIGURE EX30.14 shows a 10-cm-diameter loop in three different magnetic fields. The loop??s resistance is 0.20 Ω. For each, what are the size and direction of the induced current? a. b. c. X X
Rank in order, from largest to smallest, the three time constants τato τcfor the three circuits in FIGURE Q30.13. Explain. R R R ww ww R Circuit a L Circuit b L Circuit c L FIGURE Q30.13 ele ell
The loop in FIGURE EX30.13 is being pushed into the 0.20 T magnetic field at 50 m/s. The resistance of the loop is 0.10 Ω. What are the direction and the magnitude of the current in the loop? 50
An LC circuit oscillates at a frequency of 2000 Hz. What will the frequency be if the inductance is quadrupled?
a. Can you tell which of the inductors in FIGURE Q30.11 has the larger current through it? If so, which one? Explain.b. Can you tell through which inductor the current is changing more rapidly? If
The metal equilateral triangle in FIGURE EX30.11, 20 cm on each side, is halfway into a 0.10 T magnetic field. a. What is the magnetic flux through the triangle?b. If the magnetic field strength
An inductor with a 2.0 A current stores energy. At what current will the stored energy be twice as large?
A solenoid is wound as shown in FIGURE EX30.10. a. Is there an induced current as magnet 1 is moved away from the solenoid? If so, what is the current direction through resistor R?b. Is there an
Is the magnetic field strength in FIGURE Q30.9 increasing, decreasing, or steady? Explain. Induced E FIGURE Q30.9
There is a cw induced current in the conducting loop shown in FIGURE EX30.9. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady? X X x x x x X X X X
FIGURE Q30.8 shows a bar magnet, a coil of wire, and a current meter. Is the current through the meter right to left, left to right, or zero for the following circumstances? Explain. a. The magnet
FIGURE EX30.8 shows a 2.0-cm-diameter solenoid passing through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.20 T. What is the magnetic flux through the loop when
A bar magnet is pushed toward a loop of wire as shown in FIGURE Q30.7. Is there a current in the loop? If so, in which direction? If not, why not? N FIGURE Q30.7
What is the magnetic flux through the loop shown in FIGURE EX30.7? Magnetic field B XXXXX
FIGURE Q30.6 shows a bar magnet being pushed toward a conducting loop from below, along the axis of the loop. a. What is the current direction in the loop? Explain.b. Is there a magnetic force on
An equilateral triangle 8.0 cm on a side is in a 5.0 mT uniform magnetic field. The magnetic flux through the triangle is 6.0 μWb. What is the angle between the magnetic field and an axis
The two loops of wire in FIGURE Q30.5 are stacked one above the other. Does the upper loop have a clockwise current, a counterclockwise current, or no current at the following times? Explain. a.
FIGURE EX30.5 shows a 10 cm × 10 cm square bent at a 90? angle. A uniform 0.050 T magnetic field points downward at a 45? angle. What is the magnetic flux through the loop? 5 сm 10 ст 45 5 сm
Does the loop of wire in FIGURE Q30.4 have a clockwise current, a counterclockwise current, or no current under the following circumstances? Explain. a. The magnetic field points out of the page and
What is the magnetic flux through the loop shown in FIGURE EX30.4? x x x x . X_X xx. Xx . 1.0T 2.0T 20 cm xx"X x. XX x X Xx X X .. 20 сm 20 сm FIGURE EX30.4
A vertical, rectangular loop of copper wire is half in and half out of the horizontal magnetic field in FIGURE Q30.3. (The field is zero beneath the dashed line.) The loop is released and starts to
A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.20 Ω. Pulling the wire at a steady speed of 4.0 m/s
You want to insert a loop of copper wire between the two permanent magnets in FIGURE Q30.2. Is there an attractive magnetic force that tends to pull the loop in, like a magnet pulls on a paper clip?
A potential difference of 0.050 V is developed across the 10-cm-long wire of FIGURE EX30.2 as it moves through a magnetic field perpendicular to the page. What are the strength and direction (in or
What is the direction of the induced current in FIGURE Q30.1? FIGURE Q30.1
The earth’s magnetic field strength is 5.0 × 10-5 T. How fast would you have to drive your car to create a 1.0 V motional emf along your 1.0-m-tall radio antenna? Assume that the motion of the
An infinitely wide flat sheet of charge flows out of the page in FIGURE CP29.83. The current per unit width along the sheet (amps per meter) is given by the linear current density Js.a. What is the
A long, straight conducting wire of radius R has a nonuniform current density J = J0r/R, where J0 is a constant. The wire carries total current I.a. Find an expression for J0 in terms of I and R.b.
A flat, circular disk of radius R is uniformly charged with total charge Q. The disk spins at angular velocity ω about an axis through its center. What is the magnetic field strength at the center
a. Derive an expression for the magnetic field strength at distance d from the center of a straight wire of finite length l that carries current I.b. Determine the field strength at the center of a
You have a 1.0-m-long copper wire. You want to make an N turn current loop that generates a 1.0 mT magnetic field at the center when the current is 1.0 A. You must use the entire wire.What will be
A nonuniform magnetic field exerts a net force on a current loop of radius R. FIGURE P29.78 shows a magnetic field that is diverging from the end of a bar magnet. The magnetic field at the position
A wire along the x-axis carries current I in the negative x direction through the magnetic field a. Draw a graph of B versus x over the interval -3/2 l < x < 3/2 l.b. Find an expression for
a. In FIGURE P29.76, a long, straight, current-carrying wire of linear mass density Î¼ is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that
A conducting bar of length l and mass m rests at the left end of the two frictionless rails of length d in FIGURE P29.75. A uniform magnetic field of strength B points upward.a. In which direction,
Magnetic fields are sometimes measured by balancing magnetic forces against known mechanical forces. Your task is to measure the strength of a horizontal magnetic field using a 12-cm-long rigid metal
FIGURE P29.73 is an edge view of a 2.0 kg square loop, 2.5 m on each side, with its lower edge resting on a frictionless, horizontal surface. A 25 A current is flowing around the loop in the
The two springs in FIGURE P29.72 each have a spring constant of 10 N/m. They are compressed by 1.0 cm when a current passes through the wire. How big is the current? www 20 cm www. B=0.5 T FIGURE
The 10-turn loop of wire shown in FIGURE P29.71 lies in a horizontal plane, parallel to a uniform horizontal magnetic field, and carries a 2.0 A current. The loop is free to rotate about a
A proton in a cyclotron gains ΔK = 2eΔV of kinetic energy per revolution, where ΔV is the potential between the dees. Although the energy gain comes in small pulses, the proton makes so many
It is shown in more advanced courses that charged particles in circular orbits radiate electromagnetic waves, called cyclotron radiation. As a result, a particle undergoing cyclotron motion with
A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the
A particle of charge q and mass m moves in the uniform fields E = E0 k̂ and B = B0 k̂. At t = 0, the particle has velocity v0 = v0 î. What is the particle’s speed at a later time t?
Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight
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— 106m/s and at an angle of
FIGURE P29.64 shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio q/m. The sample is ionized, the positive
An antiproton is identical to a proton except it has the opposite charge, -e. To study antiprotons, they must be confined in an ultrahigh vacuum because they will annihilate—producing gamma
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
An antiproton (same properties as a proton except that q = -e) is moving in the combined electric and magnetic fields of FIGURE P29.61. What are the magnitude and direction of the
An electron in a cathode-ray tube is accelerated through a potential difference of 10 kV, then passes through the 2.0 cm-wide region of uniform magnetic field in FIGURE P29.60. What field strength
An electron travels with speed 1.0 Ã— 107m/s between the two parallel charged plates shown in FIGURE P29.59. The plates are separated by 1.0 cm and are charged by a 200 V battery. What
A proton moving in a uniform magnetic field with v1 = 1.00 × 106 î m/s experiences force F1 = 1.20 × 10-16 k̂ N. A second proton with v2 = 2.00 × 106 ĵ m/s experiences F2 = -4.16 × 10-16 k̂
A long, hollow wire has inner radius R1 and outer radius R2. The wire carries current I uniformly distributed across the area of the wire. Use Ampère’s law to find an expression for the magnetic

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