Revision/ Ch5/ Q4

Revision/ Ch5/ Q4

  11:04 PM    Rohit

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Q1

A conducting circular loop of radius 0.250 m is placed in the xy-plane in a uniform magnetic field of 0.360 T that points in the positive z-direction, the same direction as the normal to the plane.

(a)   Calculate the magnetic flux through the loop.

(b)   Suppose the loop is rotated clockwise around the x-axis, so the normal direction now 

        points at a 45.0° angle with respect to the z-axis. Recalculate the magnetic flux through the 

        loop.

(c)    What is the change in flux due to the rotation of the loop?

[0.0706 Wb, 0.0499 Wb, – 0.0207 Wb]

Q2

A coil with 25 turns of wire is wrapped on a frame with a square cross section 1.80 cm on a side. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 0.350 W. An applied uniform magnetic field is perpendicular to the plane of the coil, as in figure below.

(a)   If the field changes uniformly from 0.00 T to 0.500 T in 0.800 s, what is the induced emf in           the coil while the field is changing?

Find

(b)   the magnitude and

(c)    the direction of the induced current in the coil while the field is changing.

[– 5.06 ´ 10^–3 V, 1.45 ´ 10^{– 2} A]

Q3

An airplane with a wingspan of 30.0 m flies due north at a location where the downward component of Earth’s magnetic field is 0.600 3 1024 T. There is also a component pointing due north that has a magnitude of 0.470 3 1024 T.

(a)   Find the difference in potential between the wingtips when the speed of the plane is 

        2.50 ´ 10² m/s.

(b)   Which wingtip is positive?

[0.450 V, West]

Q4

(a)   The sliding bar has a length of 0.500 m and moves at 2.00 m/s in a magnetic field of   magnitude 0.250 T. Using the concept of motional emf, find the induced voltage in the   moving rod.

(b)   If the resistance in the circuit is 0.500 V, find the current in the circuit and the power   delivered to the resistor. (Note: The current in this case goes counter clockwise around the   loop.)

(c)    Calculate the magnetic force on the bar.

(d)   Use the concepts of work and power to calculate the applied force.

[0.250 V, 0.500 A, 0.125 W, 6.25 ´ 10^{– 2} N, (–)ve x-direction, 6.25 ´ 10^{– 2} N]

Q5

An AC generator consists of eight turns of wire, each having area A = 0.090 0 m², with a total resistance of 12.0 W. The coil rotates in a magnetic field of 0.500 T at a constant frequency of 60.0 Hz, with axis of rotation perpendicular to the direction of the magnetic field.

(a)   Find the maximum induced emf.

(b)   What is the maximum induced current?

(c)    Determine the induced emf and current as functions of time.

(d)   What maximum torque must be applied to keep the coil turning?

[136 V, 11.3 A, 136 V sin 377t, 11.3 sin 377t, 4.07 Nm]

Q6

(a)   Calculate the inductance of a solenoid containing 300 turns if the length of the solenoid is 25.0 cm and its cross- sectional area is 4.00 ´ 10^{– 4} m².

(b)   Calculate the self-induced emf in the solenoid described in part (a) if the current in the solenoid decreases at the rate of 50.0 A/s.

[0.181 mH, 9.05 mV]

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Revision/ Ch6/ Q5

Revision/ Ch6/ Q5

  1:45 PM    Rohit

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Problem-Solving Strategy RLC Circuits The following procedure is recommended for solving series RLC circuit problems: 1.       Calculate the inductive and capacitive reactances, XL and XC. 2.       Use XL and XC together with the resistance R to calculate the impedance Z of the          circuit. 3.       Find the maximum current or maximum voltage drop with the equivalent of  Ohm’s          law, DVmax = ImaxZ. 4.       Calculate the voltage drops across the individual elements with the appropriate          variations of Ohm’s law: DVR,max = ImaxR, DVL,max = ImaxXL, and DVC,max = ImaxXC. 5.       Obtain the phase angle using tan f = (XL – XC)/R.

Q1
An AC voltage source has an output of Dv 5 (2.00 ´ 10²) sin 2pft. This source is connected to a 1.00 ´ 10² W resistor. Find the rms voltage and rms current in the resistor.

[141 V, 1.41 A]

Q2
An 8.00 mF capacitor is connected to the terminals of an AC generator with an rms voltage of 1.50 ´ 10² V and a frequency of 60.0 Hz. Find the capacitive reactance and the rms current in the circuit.

[333 W, 0.452 A]

Q3
In a purely inductive AC circuit, L = 25.0 mH and the rms voltage is 1.50 ´ 10² V. Find the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz.

[9.42 W, 15.9 A]

Q4
A series RLC AC circuit has resistance R = 2.50 ´ 10² W, inductance L = 0.600 H, capacitance C = 3.50 mF, frequency f = 60.0 Hz, and maximum voltage DV_max = 1.50 ´ 10² V. Find
(a)   the impedance of the circuit,
(b)   the maximum current in the circuit,
(c)    the phase angle,
(d)   the maximum voltages across the elements, and
(e)   the average power delivered to the series RLC circuit

[588 W, 0.255 A, – 64.8^o, 63.8 V, 57.6 V, 193 V, 8.12 W]

Q5
Consider a series RLC circuit for which R = 1.50 ´ 10² V, L = 20.0 mH, DV_rms = 20.0 V, and f = 796 Hz.
(a)   Determine the value of the capacitance for which the rms current is a maximum.
(b)   Find the maximum rms current in the circuit.

[2.00 ´ 10^-6 Hz, 0.133 A]

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Revision/ Ch7/ Q6

Revision/ Ch7/ Q6

  4:33 PM    Rohit

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Q1

Assume a certain concave, spherical mirror has a focal length of 10.0 cm.

(a)   Locate the image and find the magnification for an object distance of 25.0 cm. Determine 

        whether the image is real or virtual, inverted or upright, and larger or smaller. Do the  

        same for object distances of

(b) 10.0 cm and

(c)  5.00 cm.

[16.7 cm, – 0.668, , – 10.0 cm, 2.00]

Q2
An object 3.00 cm high is placed 20.0 cm from a convex mirror with a focal length of magnitude 8.00 cm. Find

(a) the position of the image,

(b) the magnification of the mirror, and

(c) the height of the image.

[– 5 71 cm, 0.286, 0.858 cm]

Q3
When a woman stands with her face 40.0 cm from a cosmetic mirror, the upright image is twice as tall as her face. What is the focal length of the mirror?

[80.0 cm]

Q4
A coin 2.00 cm in diameter is embedded in a solid glass ball of radius 30.0 cm. The index of refraction of the ball is 1.50, and the coin is 20.0 cm from the surface. Find the position of the image of the coin and the height of the coin’s image.

[– 17.1 cm, 2.56 cm]

Q5
A converging lens of focal length 10.0 cm forms images of an object situated at various distances.
(a)   If the object is placed 30.0 cm from the lens, locate the image, state whether it’s real or 
       virtual, and find its magnification.
(b) Repeat the problem when the object is at 10.0 cm and
(c) again when the object is 5.00 cm from the lens.

[+ 15.0 cm, – 0.500, , – 10.0 cm, + 2.00]

Q6/ [Use lens-maker’s equation]

A thin diverging glass (index = 1.50) lens with R1 = - 3.00 m and R2 = - 6.00 m is surrounded by air. An arrow is placed 10.0 m to the left of the lens.

(a) Determine the position of the image. Repeat part (a) with the arrow and lens immersed in

(b) water (index = 1.33) and

(c) a medium with an index of refraction of 2.00.

(d) How can a lens that is diverging in air be changed into a converging lens?

[5.45 m to the left of the lens, 8.24 m to the left of the lens, 17.1 m to the left of the lens, by surrounding the lens with a medium having a refractive index greater than that of the lens material]

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Revision/ Ch 8/ Q7

Revision/ Ch 8/ Q7

  10:34 PM    Rohit

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Q1

A screen is separated from a double-slit source by 1.20 m. The distance between the two slits is 0.030 mm. The second-order bright fringe (m = 2) is measured to be 4.50 cm from the centerline. Determine

(a) the wavelength of the light and

(b) the distance between adjacent bright fringes.

[563 nm, 2.25 cm]

Q2

Semiconductors such as silicon are used to fabricate solar cells, devices that generate electric energy when exposed to sunlight. Solar cells are often coated with a transparent thin film, such as silicon monoxide (SiO; n = 1.45), to minimize reflective losses (Fig. 24.11). A silicon solar cell (n = 3.50) is coated with a thin film of SiO for this purpose. Assuming normal incidence, determine the minimum thickness of the film that will produce the least reflection at a wavelength of 552 nm.

[95.2 nm]

Q3

(a) Calculate the minimum thickness of a soap-bubble film (n = 1.33) that will result in 

       constructive interference in the reflected light if the film is illuminated by light with 

      wavelength 602 nm in free space.

(b) Recalculate the minimum thickness for constructive interference when the soap-bubble  

       film is on top of a glass slide with n = 1.50.

[113 nm, 226 nm]

Q4

Light of wavelength 5.80 ´ 10² nm is incident on a slit of width 0.300 mm. The observing screen is placed 2.00 m from the slit. Find the positions of the first dark fringes and the width of the central bright fringe.

[3.86 ´ 10^-3 m, 7.72 ´ 10^-3 m]

Q5

Monochromatic light from a helium–neon laser (l = 632.8 nm) is incident normally on a diffraction grating containing 6.00 ´ 10³ lines/cm. Find the angles at which one would observe the first-order maximum, the second-order maximum, and so forth.

[22.3^o, 49.3^o]

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Revision/ Ch 9/ Q8

Revision/ Ch 9/ Q8

  12:18 AM    Rohit

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Q1
A sodium surface is illuminated with light of wavelength 0.300 mm. The work function for sodium is 2.46eV. Calculate
(a)   the energy of each photon in electron volts,
(b)  the maximum kinetic energy of the ejected photoelectrons, and
(c)  the cut off wavelength for sodium.

[4.14 eV, 1.68 eV, 505 nm]

Q2

When monochromatic light of an unknown wavelength falls on a sample of silver, a minimum potential of 2.50 V is required to stop all of the ejected photoelectrons. Determine the

(a)   maximum kinetic energy and
(b)  maximum speed of the ejected photoelectrons.
(c)  Determine the wavelength in nm of the incident light. (The work function for silver is 4.73 
        eV.)

[2.50 eV, 9.37 ´ 10⁵ m/ s, 172 nm]

Q3

When light of wavelength 3.50 ´ 10² nm falls on a potassium surface, electrons having a maximum kinetic energy of 1.31 eV. Find

(a)   the work function of potassium,

(b)  the cutoff wavelength, and

(c)  the frequency corresponding to the cutoff wavelength.

[2.24 eV, 555 nm, 5.41 ´ 10¹⁴ Hz]

Q4

The work function for platinum is 6.35 eV.

(a)   Convert the value of the work function from electron volts to joules.

(b)  Find the cut off frequency for platinum.

(c)  What maximum wavelength of light incident on platinum releases photoelectrons from the 
       platinum’s surface?
(d) If light of energy 8.50 eV is incident on zinc, what is the maximum kinetic energy of the 
       ejected photoelectrons? Give the answer in electron volts.
(e) For photons of energy 8.50 eV, what stopping potential would be required to arrest the 
       current of photoelectrons?

[1.02 ´ 10^-18 J, 1.53 ´ 10¹⁵ Hz, 196 nm, 2.15 eV, 2.15 V]

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Revision/ Ch 10/ Q9

Revision/ Ch 10/ Q9

  11:03 PM    Rohit

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Q1
(a)   If the wavelength of an electron is 5.00 ´ 10^{- 7} m, how fast is it moving?
(b)   If the electron has a speed equal to 1.00 ´ 10⁷ m/s, what is its wavelength?

[1.46 km s^-1, 7.28 ´ 10^-11 m]

Q2

Calculate the de Broglie wavelength of a proton moving at
(a)   2.00 ´ 10⁴ m/s and
(b)   2.00 ´ 10⁷ m/s.

Q3

The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 ´ 10^{– 11} m (0.010 nm) would be required in order to “see” an atom.
(a)  If electrons were used (electron microscope), what minimum kinetic energy would be required of the electrons?

(b)  If photons were used, what minimum photon energy would be needed to obtain 1.0 ´ 10^{– 11} m resolution?

[15 keV, 1.2 ´ 10² keV]

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Revision/ Ch 11/ Q10

Revision/ Ch 11/ Q10

  9:47 PM    Rohit

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Q1

The nucleus of the deuterium atom, called the deuteron, consists of a proton and a neutron. Calculate the deuteron’s binding energy in MeV, given that its atomic mass, the mass of a deuterium nucleus plus an electron, is 2.014 102 u.

[2.224 MeV]

Q2

The half-life of the radioactive nucleus ²²⁶₈₈Ra is 1.6 ´ 10³ yr. If a sample initially contains 3.00 ´ 10¹⁶ such nuclei, determine

(a)   the initial activity in curies,

(b)   the number of radium nuclei remaining after 4.8 ´ 10³ yr, and

(c)    the activity at this later time.

[11mCi, 3.8 ´ 10¹⁵ nuclei, 1.4 mCi]

Q3

A 200.0 - mCi sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half-life of 14.0 days, how long will it keep before its activity is reduced to 20.0 mCi?

[46.5 d]

Q4

A radioactive sample contains 3.50 mg of pure 11C, which has a half-life of 20.4 min.

(a)   How many moles of 11C are present initially?

(b)   Determine the number of nuclei present initially.

(c)    What is the activity of the sample initially and after 8.00 h?

[3.18 ´ 10²⁷ mol, 1.91 ´ 10¹⁷ nuclei, 1.08 ´ 10¹⁴ Bq, 8.92 ´ 10⁶ Bq]

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