Edexcel A-Level Physics A2: Fields

[Maximum number: 9]

Some spiders may be seen suddenly moving up into the air, even when there is no wind. This happens when they let out strands of web.

The spiders are pulled upwards as the electrically charged strands of web interact with the Earth's electric field.

The average strength of the Earth's electric field is $120 \mathrm{~V} \mathrm{~m}^{-1}$ downwards.

(a)

State, with a reason, the polarity of the charge on the strands of web.

[ 1 ]

(b)

A spider moves upwards after letting out a strand of web. Determine the initial upwards acceleration of the spider.

mass of spider $=3.00\times10^{-6}\,\mathrm{kg}$

total magnitude of charge on a strand of web $=3.00\times10^{-7}\,\mathrm{C}$

[ 5 ]

Use of F=E Q

- Use of W=m g

- F-W to determine resultant force

- Use of F=m a

- $a=2.2 \mathrm{~m} \mathrm{~s}^{-2}$

Example of calculation
$\begin{aligned} & F=120 \mathrm{~V} \mathrm{~m}^{-1} \times 3.00 \times 10^{-7} \mathrm{C}=3.60 \times 10^{-5} \mathrm{~N} & W=3.00 \times 10^{-6} \mathrm{~kg} \times 9.81 \mathrm{Nkg}^{-1}=2.94 \times 10^{-5} \mathrm{~N} & \text { Resultant force }=3.60 \times 10^{-5} \mathrm{~N}-2.94 \times 10^{-5} \mathrm{~N}=6.57 \times 10^{-6} \mathrm{~N} & a=6.57 \times 10^{-6} \mathrm{~N} \div 3.00 \times 10^{-6} \mathrm{~kg} & =2.19 \mathrm{~m} \mathrm{~s}^{-2} \end{aligned}$

(5)

(c)

The Earth has an electric field because charge is distributed over its surface.

Determine the quantity of charge on $1 \mathrm{~m}^{2}$ of the Earth's surface which would cause an electric field of $120 \mathrm{~V} \mathrm{~m}^{-1}$ .

You should assume that the charge is distributed evenly.
radius of Earth $=6400 \mathrm{~km}$

[ 3 ]

Use $E=Q/(4\pi\varepsilon_0r^2)$ or $E=kQ/r^2$ , and $A=4\pi r^2$ .

$120=(8.99\times10^9)Q/(6.4\times10^6)^2$ , so $Q=5.47\times10^5\,\mathrm{C}$ . The surface area is $5.15\times10^{14}\,\mathrm{m^2}$ , giving $Q/A=1.1\times10^{-9}\,\mathrm{C\,m^{-2}}$ .

[Maximum number: 4]

The surface of a balloon can become charged by rubbing it against clothing. The charge on the surface of the balloon can be assumed to act as if it was concentrated at the balloon's centre.

Two balloons are suspended by cotton threads so that they just touch each other as shown in diagram 1. The two balloons are then given an equal negative charge and repel as shown in diagram 2. The dots represent the centre of each balloon.

Diagram 1

Diagram 2

(a)

Show that the charge on each balloon is about 2 × 10^-7 C.

[ 2 ]

Use Coulomb's law, $F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q^2}{r^2}=k\dfrac{Q^2}{r^2}$ . Thus $1.16\times10^{-3}=(8.99\times10^9)Q^2/(0.47)^2$ , giving $Q=1.69\times10^{-7}\,\mathrm{C}$ , about $2\times10^{-7}\,\mathrm{C}$ .

(b)

One balloon is removed and the remaining balloon returns to its original position.

Calculate the electric potential at a distance of 0.30 m from the centre of the remaining balloon.

Electric potential =

[ 2 ]

Use $V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r}=kQ/r$ . With the balloon negatively charged, $V=(8.99\times10^9)(-1.7\times10^{-7})/0.30=-5.09\times10^3\,\mathrm{V}$ , about $-5100\,\mathrm{V}$ .

[Maximum number: 7]

In the early 20th century, experiments were carried out in which alpha particles were directed towards thin gold foil.

A simplified diagram of the apparatus used is shown.

Figure for Question 3 — Edexcel A-Level Physics A2

(a)

One experiment used gold foil made from the gold isotope ${ }_{79}^{197} \mathrm{Au}$ . The alpha particles had an initial kinetic energy of 4.7 MeV .

[ 7 ]

(i)

Show that the closest distance these alpha particles can get to a gold nucleus is about 5 x 10^-14 m.

[ 4 ]

Convert $4.7\,\mathrm{MeV}$ to $7.52\times10^{-13}\,\mathrm J$ , then equate this to the electrostatic potential energy: $7.52\times10^{-13}=\frac{(8.99\times10^9)(2e)(79e)}{r}.$ This gives $r=4.8\times10^{-14}\,\mathrm m$ , about $5\times10^{-14}\,\mathrm m$ .

(ii)

Calculate the strength of the electric field due to the gold nucleus at this distance.

Strength of electric field =

[ 3 ]

Use $E=kQ/r^2$ , with Q=79e: $E=\frac{(8.99\times10^9)(79)(1.60\times10^{-19})}{(4.8\times10^{-14})^2}=4.9\times10^{19}\,\mathrm{N\,C^{-1}}.$

[Maximum number: 1]

Some spiders may be seen suddenly moving up into the air, even when there is no wind. This happens when they let out strands of web.

The spiders are pulled upwards as the electrically charged strands of web interact with the Earth's electric field.

The average strength of the Earth's electric field is $120 \mathrm{~V} \mathrm{~m}^{-1}$ downwards.

State, with a reason, the polarity of the charge on the strands of web.

[Maximum number: 5]

Some spiders may be seen suddenly moving up into the air, even when there is no wind. This happens when they let out strands of web.

The spiders are pulled upwards as the electrically charged strands of web interact with the Earth's electric field.

The average strength of the Earth's electric field is $120 \mathrm{~V} \mathrm{~m}^{-1}$ downwards.

A spider moves upwards after letting out a strand of web. Determine the initial upwards acceleration of the spider.

mass of spider $=3.00\times10^{-6}\,\mathrm{kg}$

total magnitude of charge on a strand of web $=3.00\times10^{-7}\,\mathrm{C}$

Use of F=E Q

- Use of W=m g

- F-W to determine resultant force

- Use of F=m a

- $a=2.2 \mathrm{~m} \mathrm{~s}^{-2}$

Example of calculation
$\begin{aligned} & F=120 \mathrm{~V} \mathrm{~m}^{-1} \times 3.00 \times 10^{-7} \mathrm{C}=3.60 \times 10^{-5} \mathrm{~N} & W=3.00 \times 10^{-6} \mathrm{~kg} \times 9.81 \mathrm{Nkg}^{-1}=2.94 \times 10^{-5} \mathrm{~N} & \text { Resultant force }=3.60 \times 10^{-5} \mathrm{~N}-2.94 \times 10^{-5} \mathrm{~N}=6.57 \times 10^{-6} \mathrm{~N} & a=6.57 \times 10^{-6} \mathrm{~N} \div 3.00 \times 10^{-6} \mathrm{~kg} & =2.19 \mathrm{~m} \mathrm{~s}^{-2} \end{aligned}$

(5)

[Maximum number: 2]

The surface of a balloon can become charged by rubbing it against clothing. The charge on the surface of the balloon can be assumed to act as if it was concentrated at the balloon's centre.

Two balloons are suspended by cotton threads so that they just touch each other as shown in diagram 1. The two balloons are then given an equal negative charge and repel as shown in diagram 2. The dots represent the centre of each balloon.

Diagram 1

Diagram 2

Show that the charge on each balloon is about 2 × 10^-7 C.

Use Coulomb's law, $F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q^2}{r^2}=k\dfrac{Q^2}{r^2}$ . Thus $1.16\times10^{-3}=(8.99\times10^9)Q^2/(0.47)^2$ , giving $Q=1.69\times10^{-7}\,\mathrm{C}$ , about $2\times10^{-7}\,\mathrm{C}$ .

[Maximum number: 3]

In the early 20th century, experiments were carried out in which alpha particles were directed towards thin gold foil.

A simplified diagram of the apparatus used is shown.

Figure for Question 7 — Edexcel A-Level Physics A2

One experiment used gold foil made from the gold isotope ${ }_{79}^{197} \mathrm{Au}$ . The alpha particles had an initial kinetic energy of 4.7 MeV .

Calculate the strength of the electric field due to the gold nucleus at this distance.

Strength of electric field =

Use $E=kQ/r^2$ , with Q=79e: $E=\frac{(8.99\times10^9)(79)(1.60\times10^{-19})}{(4.8\times10^{-14})^2}=4.9\times10^{19}\,\mathrm{N\,C^{-1}}.$

[Maximum number: 1]

The electric potential V varies with the distance r from a charged object as shown.

At which distance, A, B, C or D, does the electric field strength have its maximum value?

Figure for Question 8 — Edexcel A-Level Physics A2

[Maximum number: 3]

A spark chamber consists of a set of parallel metal plates. It can reveal the path of a high energy particle as shown.

Figure for Question 9 — Edexcel A-Level Physics A2

A potential difference of 10.5 kV is applied across two adjacent plates as shown below.

A high energy particle causes ionisation of the atoms in the space between the plates.

Show that the force on an ionised atom due to the electric field is
about $2.6 \times 10^{-13} \mathrm{~N}$ .
charge on ionised atom $=1.60 \times 10^{-19} \mathrm{C}$
distance between plates $=6.40 \mathrm{~mm}$

Use E=V/d and F=EQ. Hence $F=(10500/0.00640)(1.60\times10^{-19})=2.63\times10^{-13}\,\mathrm{N}$ , about $2.6\times10^{-13}\,\mathrm{N}$ .

[Maximum number: 4]

In the early 20th century, experiments were carried out in which alpha particles were directed towards thin gold foil.

A simplified diagram of the apparatus used is shown.

Figure for Question 10 — Edexcel A-Level Physics A2

One experiment used gold foil made from the gold isotope ${ }_{79}^{197} \mathrm{Au}$ . The alpha particles had an initial kinetic energy of 4.7 MeV .

Show that the closest distance these alpha particles can get to a gold nucleus is about 5 x 10^-14 m.

Convert $4.7\,\mathrm{MeV}$ to $7.52\times10^{-13}\,\mathrm J$ , then equate this to the electrostatic potential energy: $7.52\times10^{-13}=\frac{(8.99\times10^9)(2e)(79e)}{r}.$ This gives $r=4.8\times10^{-14}\,\mathrm m$ , about $5\times10^{-14}\,\mathrm m$ .

[Maximum number: 3]

A spark chamber consists of a set of parallel metal plates. It can reveal the path of a high energy particle as shown.

Figure for Question 11 — Edexcel A-Level Physics A2

A potential difference of 10.5 kV is applied across two adjacent plates as shown below.

Sketch lines to represent the electric field between the plates.

[Maximum number: 3]

A student built the circuit shown. The capacitor was initially uncharged.

Figure for Question 12 — Edexcel A-Level Physics A2

She closed the switch and plotted a graph of current on ammeter $\mathrm{A}_{1}$ against time.

Determine the capacitance of the capacitor.

Capacitance =

Use $I=I_0e^{-t/(RC)}$ with two corresponding graph values, or use the time constant $\tau=RC$ . For example, $0.04=0.15e^{-10/(33\,000C)}$ , giving $C=2.27\times10^{-4}\,\mathrm{F}$ . Accept $2.0\times10^{-4}$ to $2.3\times10^{-4}\,\mathrm{F}$ .

[Maximum number: 5]

A student carried out an investigation to compare the energy stored in a mechanical mouse trap with the energy stored in an electronic mouse trap.

The student tested the capacitor by charging it until the p.d. across the capacitor was 600 V and recording the p.d. as it was discharged through a resistor of resistance $3000 \Omega$ .

The following graph was obtained.

Figure for Question 13 — Edexcel A-Level Physics A2

Determine whether the mechanical or the electric mouse trap stores the most energy.

Read the time constant from the graph: $RC=4.5\,\mathrm{s}$ . With $R=3000\,\Omega$ , $C=1.5\times10^{-3}\,\mathrm{F}$ . Therefore $W=\tfrac12CV^2=\tfrac12(1.5\times10^{-3})(600)^2=270\,\mathrm{J}$ , much greater than $0.47\,\mathrm{J}$ , so the electronic trap stores more energy.

Figure for Answer to Question 13 — Edexcel A-Level Physics A2

[Maximum number: 4]

A student built the circuit shown. The capacitor was initially uncharged.

Figure for Question 14 — Edexcel A-Level Physics A2

She closed the switch and plotted a graph of current on ammeter $\mathrm{A}_{1}$ against time.

(a)

Explain how the current on ammeter A_2 would vary over the same time interval.

[ 2 ]

(b)

Determine the charge stored on the capacitor after 30 s .

Charge stored on capacitor after $30 \mathrm{~s}=$

[ 2 ]

Determine the area under the current–time curve, giving $Q\approx1.1\times10^{-3}\,\mathrm{C}$ (acceptable range $1.0\times10^{-3}$ to $1.2\times10^{-3}\,\mathrm{C}$ ). Alternatively, use Q=CV with $V=5.0\,\mathrm{V}$ .

[Maximum number: 3]

Two identical capacitors were connected in series and charged. They were then discharged through a resistor and ammeter.
A student investigated how the current in the resistor varied as the capacitors discharged.

Draw an appropriate circuit diagram for this investigation.

[Maximum number: 6]

Two identical capacitors were connected in series and charged. They were then discharged through a resistor and ammeter.
A student investigated how the current in the resistor varied as the capacitors discharged.

The student had a stopwatch.

Describe how the student should determine an accurate value for the total capacitance of the capacitors.

Award any six valid method points. Choose a resistor giving a reasonable discharge time;
measure its resistance;
charge the series capacitors to a known initial p.d.;
start timing when switching to discharge;
record current and time simultaneously as closely as possible;
take many readings over at least a half-life or time constant.

A graphical route may plot $\ln I$ against t, for which the gradient is -1/(RC);
or obtain $t_{1/2}$ from an I–t graph and use $t_{1/2}=RC\ln2$ ;
or obtain the time to reach $37\%$ and use $\tau=RC$ .

A non-graphical route may repeat at least three times and average the measured half-life or time constant before using the same formulae.

[Maximum number: 1]

Which of the following is a possible unit for magnetic flux?

A

$\mathrm{Tm}{ }^{2}$

B

$\mathrm{Tm}^{-2}$

C

$\mathrm{Wbm}^{2}$

D

$\mathrm{Wbm}^{-2}$

[Maximum number: 3]

In 1932, Carl Anderson published this photograph of a track in a cloud chamber. The cloud chamber contained a lead plate. There was a magnetic field perpendicular to the plane of the track.

Figure for Question 18 — Edexcel A-Level Physics A2

The photograph shows the track of a positron from cosmic rays and is the first photographic record of the existence of an antiparticle.

Deduce the direction of the magnetic field.

Direction of magnetic field =

[Maximum number: 3]

A music system has a number of loudspeakers. One loudspeaker produces the low frequency sounds. This loudspeaker consists of a coil connected to a cone. The coil is in a region of magnetic field produced by a permanent magnet, as shown.

Figure for Question 19 — Edexcel A-Level Physics A2

Explain how an alternating current in the coil causes the cone to oscillate with the frequency of the alternating current.

[Maximum number: 6]

*16 A bar magnet was dropped vertically through a small coil, as shown.

Figure for Question 20 — Edexcel A-Level Physics A2

The coil was attached to a data logger. The data logger recorded the variation of e.m.f. across the coil with time.

The output from the data logger is shown below.

Explain the variation of e.m.f. with time.

[Maximum number: 6]

A student carried out an investigation to compare the energy stored in a mechanical mouse trap with the energy stored in an electronic mouse trap.

The electronic mouse trap works by applying a large potential difference (p.d.) across two metal plates. The diagram shows part of the circuit for the electronic mouse trap.

Figure for Question 21 — Edexcel A-Level Physics A2

The transformer T consists of two coils wound around a single iron core. An alternating p.d. is applied to the input coil and the output coil is connected, through a diode, to a capacitor.

Explain how applying a p.d. across the input coil causes the capacitor to charge.

[Maximum number: 3]

A student carried out an investigation to compare the energy stored in a mechanical mouse trap with the energy stored in an electronic mouse trap.

The electronic mouse trap works by applying a large potential difference (p.d.) across two metal plates. The diagram shows part of the circuit for the electronic mouse trap.

Figure for Question 22 — Edexcel A-Level Physics A2

The graph shows how the magnetic flux density B in the iron core varies with time.

Show that the maximum p.d. across the output coil is about 600 V .
number of turns on coil = 1700
cross-sectional area of coil $=3.5 \times 10^{-4} \mathrm{~m}^{2}$

Edexcel A-Level Physics A2 4.4 Electric and Magnetic Fields Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question (a)

Question (b)

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22