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LSN 5-6 TO 5-8 TEST REVIEW

4.This question is about forces on charged particles.

(a)A charged particle is situated in a field of force. Deduce the nature of the force-field (magnetic, electric or gravitational) when the force on the particle

(i)is along the direction of the field regardless of its charge and velocity;

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(ii)is independent of the velocity of the particle but depends on its charge;

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(iii)depends on the velocity of the particle and its charge.

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(5)

(b)An electron is accelerated from rest in a vacuum through a potential difference of 2.1 kV. Deduce that the final speed of the electron is 2.7 × 107m s–1.

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(3)

The electron in (b) then enters a region of uniform electric field between two conducting horizontal metal plates as shown below.

The electric field outside the region of the plates may be assumed to be zero. The potential difference between the plates is 95 V and their separation is 2.2 cm.

As the electron enters the region of the electric field, it is travelling parallel to the plates.

(c)(i)On the diagram above, draw an arrow at P to show the direction of the force due to the electric field acting on the electron.

(1)

(ii)Calculate the force on the electron due to the electric field.

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(3)

(d)The plates in the diagram above are of length 12 cm. Determine

(i)the time of flight between the plates.

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(1)

(ii)the vertical distance moved by the electron during its passage between the plates.

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(3)

(e)Suggest why gravitational effects were not considered when calculating the deflection of the electron.

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(2)

(f)In a mass spectrometer, electric and magnetic fields are used to select charged particles of one particular speed. A uniform magnetic field is applied in the region between the plates, such that the electron passes between the plates without being deviated.

For this magnetic field,

(i)state and explain its direction;

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(3)

(ii)determine its magnitude.

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(2)

(g)The electric and magnetic fields in (f) remain unchanged. Giving a brief explanation in each case, compare qualitatively the deflection of the electron in (f) with that of

(i)an electron travelling at a greater initial speed;

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(ii)a proton having the same speed;

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(iii)an alpha particle (α-particle) having the same speed.

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(7)

31.Magnetic and electric fields

A proton is accelerated from rest in a vacuum through a potential difference of 420 V. The proton then enters a region ABCD of uniform magnetic field as shown.

The magnetic field is directed into the plane of the paper. The field strength is 15 mT.

(a)(i)Calculate the speed of the proton as it enters the region of the magnetic field.

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(2)

(ii)The path of the proton as drawn on the diagram is in the plane of the paper. The proton enters the region ABCD of the magnetic field and leaves through the side BC. On the diagram above, draw the path of the proton within and beyond the region ABCD of the magnetic field. Label the path P.

(2)

(iii)Determine the magnitude of the force due to the magnetic field that acts on the proton while the proton is in the region ABCD.

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(2)

(b)(i)Define electric field strength at a point.

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(2)

(ii)Determine the magnitude of the electric field strength that would produce a force on a proton that is equal to the force calculated in (a)(iii).

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(2)

(iii)The electric field calculated in (b)(ii) is applied in the region ABCD. The electric field is arranged such that, when a proton enters the region, the force due to the electric field is opposite in direction to the force due to the magnetic field. Suggest, with a reason, the path that the proton will follow in the region ABCD.

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(2)

73.A circular coil of wire of radius r is placed in a uniform magnetic field of flux density B. The angle between the plane of the coil and the magnetic field is θ.

The magnetic flux linking the coil is

A.πr2B.

B.πr2B sin θ.

C.πr2B cos θ.

D.πr2B.

(1)

75.Two long, vertical wires X and Y carry currents in the same direction and pass through a horizontal sheet of card.

Iron filings are scattered on the card. Which one of the following diagrams best shows the pattern formed by the iron filings? (The dots show where the wires X and Y enter the card.)

(1)

83.An electron is moving in air at right angles to a uniform magnetic field. The diagram below shows the path of the electron. The electron is slowing down.

Which one of the following correctly gives the direction of motion of the electron and the direction of the magnetic field?

Direction of motion / Direction of magnetic field
A. / clockwise / into plane of paper
B. / clockwise / out of plane of paper
C. / anti-clockwise / into plane of paper
D. / anti-clockwise / out of plane of paper

(1)

86.A metal ring is placed in a region of uniform magnetic field such that the plane of the ring is perpendicular to the direction of the field. The field strength is increasing at a constant rate.

The sketch-graph shows the variation with time t of the magnetic flux  linking the ring.

Which of the following graphs best shows the variation with time t of the induced current I in the ring?

(1)

87.Electromagnetic induction

(a)State Faraday’s law of electromagnetic induction.

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(1)

(b)A long straight wire carries a constant current. A rectangular loop of conducting wire is placed near the wire such that the wire is on the plane of the loop. The loop is then moved at constant speed away from the wire as shown in the diagram below.

(i)Explain why an emf is induced in the loop.

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(2)

(ii)On the diagram above, draw an arrow to indicate the direction of the current induced in the loop. Explain your answer.

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(2)

(iii)Energy is dissipated in the wire of the loop. Explain how the movement of the loop gives rise to energy dissipation.

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(3)

89.A positively charged particle enters a region of uniform magnetic field. The direction of the particle’s velocity is parallel to the direction of the magnetic field as shown in the diagram below.

Which of the following diagrams correctly shows the path of the charged particle while in the region of magnetic field?

(1)

90.A transformer has a primary coil with Np turns and a secondary coil with Ns turns. An alternating voltage supply of frequency f and r.m.s. value Vp is connected to the primary coil.

Which of the following correctly gives the frequency and r.m.s. voltage in the secondary coil?

Frequency / Voltage
A. / /
B. / f /
C. / /
D. / f /

(1)

92.This question is about induced e.m.f.

A small area A is in a region of uniform magnetic field of strength B. The field makes an angle  to the normal to the area as shown below.

(a)With reference to the diagram, define magnetic flux both in words and in symbols.

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(2)

(b)A thin copper ring encloses an area of 1.8×10–3 m2. The plane of the ring is normal to a uniform magnetic field. The magnetic field strength increases at a constant rate of
5.0×10–2 T s–1.

Calculate the e.m.f. induced in the ring.

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(2)

94.Drops of a liquid are being sprayed vertically upwards into the air by a hose in a region where the Earth’s magnetic field is directed horizontally as shown in the diagram below.

As each drop leaves the hose it becomes negatively charged. Which of the following describes the direction of the magnetic force acting on the drops?

A.Downwards

B.Upwards

C.Out of the paper

D.Into the paper

(1)

95.When a coil is rotated in a uniform magnetic field at a certain frequency, the variation with time t of the induced emf E is as shown below.

The frequency of rotation of the coil is reduced to one half of its initial value. Which one of the following graphs correctly shows the new variation with time t of the induced emf E?

(1)

97.A bar magnet is suspended above a coil of wire by means of a spring, as shown below.

The ends of the coil are connected to a sensitive high resistance voltmeter. The bar magnet is pulled down so that its north pole is level with the top of the coil. The magnet is released and the variation with time t of the velocity v of the magnet is shown below.

(a)On the diagram above,

(i)mark with the letter M, one point in the motion where the reading of the voltmeter is a maximum;

(ii)mark with the letter Z, one point where the reading on the voltmeter is zero.

(2)

(b)Explain, in terms of changes in flux linkage, why the reading on the voltmeter is alternating.

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(2)

99.A uniform magnetic field of strength B completely links a coil of area S. The field makes an angle  to the plane of the coil.

The magnetic flux linking the coil is

A.BS.

B.BS cos .

C.BS sin .

D.BS tan .

(1)

100.A resistor is connected in series with an alternating current supply of negligible internal resistance. The peak value of the supply voltage is Vo and the peak value of the current in the resistor is I0. The average power dissipation in the resistor is

C..

D.2.

(1)

102.The rms voltages across the primary and secondary coils in an ideal transformer are Vp and Vs respectively. The currents in the primary and secondary coils are Ip and Is respectively.

Which one of the following statements is always true?

A.Vs= Vp

B.Is = Ip

C.VsIs = VpIp

D..

(1)

105.Faraday’s law of electromagnetic induction states that the induced emf is

A.proportional to the change in magnetic flux linkage.

B.proportional to the rate of change of magnetic flux linkage.

C.equal to the change in magnetic flux linkage.

D.equal to the change of magnetic flux.

(1)

107.The variation with time t of the magnetic flux Φ through a coil is shown below.

Which of the following diagrams best shows the variation with time t of the emf E induced in the coil?

(1)

113.A resistor of resistance R is connected in series with a sinusoidal alternating supply having a maximum value of emf V0.

The best estimate for the average power dissipated in the resistor during one cycle of the alternating current is

(1)

115.This question is about an ideal transformer.

(a)State Faraday’s law of electromagnetic induction.

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(2)

(b)The diagram below shows an ideal transformer.

(i)Use Faraday’s law to explain why, for normal operation of the transformer, the current in the primary coil must vary continuously.

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(2)

(ii)Outline why the core is laminated.

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(2)

(iii)The primary coil of an ideal transformer is connected to an alternating supply rated at 230V. The transformer is designed to provide power for a lamp rated as 12V, 42W and has 450 turns of wire on its secondary coil. Determine the number of turns of wire on the primary coil and the current from the supply for the lamp to operate at normal brightness.

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(3)

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