IB Physics HL D Fields

[Maximum number: 13]

This question is in two parts. Part 1 is about gravitational force fields. Part 2 is about properties of a gas.

(a)

State Newton's universal law of gravitation.

[ 2 ]

(b)

A satellite of mass m orbits a planet of mass M. Derive the following relationship between the period of the satellite T and the radius of its orbit R (Kepler's third law).

T^{2}=\frac{4 \pi^{2} R^{3}}{G M}

[ 3 ]

$G \frac{M m}{R^{2}}=\frac{m v^{2}}{R}$ so $v^{2}=\frac{G m}{R}$ ;
$v=\frac{2 \pi R}{T} ;$ $\left(v^{2}=\right) \frac{4 \pi^{2} R^{2}}{T^{2}}=\frac{G m}{R} ;$
or
$G \frac{M m}{R^{2}}=m \omega^{2} R ;$ $\omega^{2}=\frac{4 \pi^{2}}{T^{2}} ;$ $\frac{4 \pi^{2}}{T^{2}}=\frac{G M}{R^{3}} ;$

Marking guidance:

Award [3] to a clear response with a missing step.

(c)

A polar orbiting satellite has an orbit which passes above both of the Earth's poles. One polar orbiting satellite used for Earth observation has an orbital period of $6.00 \times 10^{3} \mathrm{~s}$ .

\begin{array}{ll} \text { Mass of Earth } & =5.97 \times 10^{24} \mathrm{~kg} \\ \text { Average radius of Earth } & =6.37 \times 10^{6} \mathrm{~m} \end{array}

[ 8 ]

(i)

Using the relationship in (b), show that the average height above the surface of the Earth for this satellite is about 800 km .

[ 3 ]

$\quad R^{3}=\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24} \times 6000^{2}}{4 \times \pi^{2}}$ ;

\begin{aligned} & R=7.13 \times 10^{6}(\mathrm{~m}) \\ & h=\left(7.13 \times 10^{6}-6.37 \times 10^{6}\right)=760(\mathrm{~km}) \end{aligned}

Award [3] for an answer of 740 with $\pi$ taken as 3.14.

(ii)

The satellite moves from an orbit of radius 1200 km above the Earth to one of radius 2500 km . The mass of the satellite is 45 kg .

Calculate the change in the gravitational potential energy of the satellite.

[ 3 ]

clear use of $\Delta V=\frac{\Delta E}{m}$ and $V=-\frac{G m}{r}$ or $\Delta E=G M m\left(\frac{1}{r_{1}}-\frac{1}{r_{2}}\right)$ ;
one value of potential energy calculated $\left(2.37 \times 10^{9}\right.$ or $\left.2.02 \times 10^{9}\right)$ ;

Marking guidance:

Award [3] for a bald correct answer.

(iii)

Explain whether the gravitational potential energy has increased, decreased or stayed the same when the orbit changes, as in (c)(ii).

[ 2 ]

increased; further from Earth / closer to infinity / smaller negative value;

Part 2 Properties of a gas
(a) ( Q ) energy transferred between two objects (at different temperatures);
( U ) (total) potential energy and (random) kinetic energy of the molecules/particles (of the gas);
(b) (i) use of area within cycle;
each large square has work value of 250 J ;
estimate $(16 \times 250=) 4000 \mathrm{~J}$ ; (allow 3600 - 4100)
(ii) (work is done by the gas because) area under expansion is greater than that under compression/pressure during expansion is greater than during compression;
(iii) clear attempt to compare two P V values; evaluate two P V values correctly eg $75 \times 80=6000$ and $200 \times 30=6000$ ;
(iv) use of P V=n R T or equivalent;
$1350 / 1330 \mathrm{~K}$ ;
(v) both changes are isochoric/isovolumetric/constant volume changes;

B: temperature/internal energy increases, D: temperature/internal energy decreases;
B: thermal energy/heat input (to system), D: thermal energy/heat output (from system);
B: pressure increases, D: pressure decreases;

[Maximum number: 2]

Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

Figure for Question D. Fields question 2 — IB Physics HL

The mass of ions ejected each second is $6.6 \times 10^{-6} \mathrm{~kg}$ and the speed of each ion is $5.2 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}$ . The initial total mass of the spacecraft and its fuel is 740 kg . Assume that the ions travel away from the spacecraft parallel to its direction of motion.

In practice, the ions leave the spacecraft at a range of angles as shown.

Outline why the ions are likely to spread out.

[Maximum number: 14]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

(a)

Define electric field strength.

[ 2 ]

(b)

(b) The diagram shows a pair of horizontal metal plates. Electrons can be deflected vertically using an electric field between the plates.

[ 5 ]

(i)

Label, on the diagram, the polarity of the metal plates which would cause an electron positioned between the plates to accelerate upwards.

[ 1 ]

(ii)

Draw the shape and direction of the electric field between the plates on the diagram.

[ 2 ]

(iii)

Calculate the force on an electron between the plates when the electric field strength has a value of $2.5 \times 10^{3} \mathrm{NC}^{-1}$ .

[ 2 ]

$F=2.5 \times 10^{3} \times 1.6 \times 10^{-19}$ ;
$4.0 \times 10^{-16} \mathrm{~N}$ ;

Marking guidance:

Award [2] for a bald correct answer.

(c)

The diagram shows two isolated electrons, X and Y , initially at rest in a vacuum. The initial separation of the electrons is 5.0 mm . The electrons subsequently move apart in the directions shown.

[ 7 ]

(i)

Show that the initial electric force acting on each electron due to the other electron is approximately $9 \times 10^{-24} \mathrm{~N}$ .

[ 2 ]

(c) (i) use of $F=\frac{\left(1.60 \times 10^{-19}\right)^{2}}{4 \pi \varepsilon_{0}\left(5.0 \times 10^{-3}\right)^{2}}$ or $F=\frac{\left(1.60 \times 10^{-19}\right)^{2}}{\left(5.0 \times 10^{-3}\right)^{2}} \times 8.99 \times 10^{9}$ ;
$9.2 \times 10^{-24} \mathrm{~N} ;$

(ii)

Discuss the motion of one electron after it begins to move.

[ 3 ]

(iii)

The diagram shows Y as seen from X , at one instant. Y is moving into the plane of the paper. For this instant, draw on the diagram the shape and direction of the magnetic field produced by Y .

[ 2 ]

[Maximum number: 6]

(a)

A conducting rod of length L is moved with speed v at right angles to a uniform magnetic field of flux density B. The field is directed into the plane of the page.

[ 3 ]

(i)

Show, using Faraday's law or otherwise, that the potential difference, V, established between the ends of the rod is V=v B L.

[ 3 ]

ALTERNATE 1

In time $\Delta t$ , rod moves a distance $v \Delta t$

Flux increases by $B(L v \Delta t)^{}$

«By Faraday» induced emf is the rate of change of flux: $\frac{B L v \Delta t}{\Delta t}$

«=BLv»

ALTERNATE 2

<<From $\varepsilon=-\frac{N \Delta \Phi}{\Delta t} \gg$

Recognition that $\Phi=B A$

Recognition that N = 1

Recognition that $\frac{\Delta A}{\Delta t}=L v \vee$

<<Leading to V=vBL OR $\varepsilon=\mathrm{BLv}>$

ALTERNATE 3

«In steady state» electrons stop drifting and so net force is zero q v B=q E

Substitution of $E=\frac{V}{L}$ to get result

ALT 1: Correct MP2 scores MP1

ALT2:

V and $\varepsilon$ are interchangeable. Ignore negative sign.

[3]

(b)

A coil is rotating in a region of magnetic field with angular speed $12.56 \mathrm{rad} \mathrm{s}^{-1}$ . At t=0, the field is parallel to the surface of the coil.

[ 3 ]

(i)

State the magnetic flux linkage through the coil at t=0.

[ 1 ]

(ii)

Draw, on the axes, a graph to show the variation with time of the induced emf in the loop. (No numbers are required on the vertical axis.)
emf

Figure for Question (ii) — IB Physics HL

[ 2 ]

IB Physics HL D: Fields

Covered syllabus points

Covered syllabus points

D. Fields question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (iii)

D. Fields question 2

D. Fields question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)

Question (i)

Question (ii)

Question (iii)

D. Fields question 4

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)