IB Physics SL D: Fields

Practise IB Physics SL fields through electric, gravitational and magnetic interactions, interpreting field diagrams and applying equations to data.

Covered syllabus points

D.1 Gravitational fields D.2 Electric and magnetic fields D.3 Motion in electromagnetic fields

[Maximum number: 3]

A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.

Figure for Question D. Fields question 1 — IB Physics SL

The satellite is orbiting the Earth at a distance of 6600 km from the centre of the Earth.

Determine the orbital period for the satellite.

Mass of Earth $=6.0 \times 10^{24} \mathrm{~kg}$

$\begin{aligned} & \frac{m v^{2}}{r}=G \frac{M m}{r^{2}} & \text { leading to } T^{2}=\frac{4 \pi^{2} r^{3}}{G M} & T=5320 \text { «s» } \end{aligned}$

Alternative 2
$\begin{aligned} & \text { « } V=\sqrt{\frac{G m_{E}}{r}} \text { » }=\sqrt{\frac{6.67 \times 10^{-11} \times 6.0 \times 10^{24}}{6600 \times 10^{3}}} \text { OR } 7800 \text { « } \mathrm{ms}^{-1} \text { » } & \text { distance }=2 \pi r=2 \pi \times 6600 \times 10^{3} \text { « } \mathrm{m} \text { » or } 4.15 \times 10^{7} \text { « } \mathrm{m} \text { » } & \text { « } T=\frac{d}{v}=\frac{4.15 \times 10^{7}}{7800} \text { » }=5300 \text { « } \mathrm{S} \text { » } \end{aligned}$

Accept use of $\omega$ nistead of v

[Maximum number: 5]

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 SL

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.

(a)

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

[ 2 ]

(i)

Outline why the ions are likely to spread out.

[ 2 ]

(b)

On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.

[ 3 ]

(i)

Outline what is meant by the gravitational field strength at a point.

[ 2 ]

(ii)

Newton's law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.

[ 1 ]

[Maximum number: 5]

Two oppositely charged parallel plates are a distance 8.0 cm apart. The potential difference between the plates is 120 V . An alpha particle is placed on the positively charged plate and released from rest. Gravity is ignored.

Figure for Question D. Fields question 3 — IB Physics SL

(a)

Calculate the electric field between the plates.

[ 1 ]

$E=\ll \frac{120}{8.0 \times 10^{-2}}=>1.5 \times 10^{3} N C^{-1} \boldsymbol{O} \boldsymbol{R} \mathrm{Vm}^{-1}$

[1]

(b)

Show that the acceleration of the alpha particle is about $7 \times 10^{10} \mathrm{~ms}^{-2}$ .

[ 2 ]

$\begin{aligned} F=<e E=>3.2 \times 10^{-19} \times 1.5 \times 10^{3} \text { OR } 4.8 \times 10^{-16} \mathrm{~N} a=<\frac{F}{m}=>\frac{4.8 \times 10^{-16}}{4 \times 1.67 \times 10^{-27}} \text { OR } 7.2 \times 10^{10} \mathrm{~ms}^{-2} \quad \end{aligned}$

Allow ECF from a).

Award [1] if they use a charge of e and a mass of 2 u obtaining the right result.

[2]

(c)

A magnetic field directed into the plane of the page is now established between the plates. An alpha particle enters the region between the plates with a horizontal speed of $5.0 \times 10^{5} \mathrm{~m} \mathrm{~s}^{-1}$ . The particle is not deflected.

Calculate the magnitude of the magnetic field.

[ 2 ]

$\begin{aligned} F_{\mathrm{m}} =F_{\mathrm{e}} \text { OR } q v B=q E \text { OR } B=F_{\mathrm{e}} / q v \quad B =\ll \frac{E}{v}=\frac{1.5 \times 10^{3}}{5.0 \times 10^{5}}=>3.0 \times 10^{-3} T \end{aligned}$

Award [2] if $3.0 \times 10^{-3}$ « T » is seen as the answer without working.

Allow ECF from a) and b) i)

[2]

[Maximum number: 8]

(a)

State Newton's universal law of gravitation.

[ 3 ]

(b)

Deduce that the gravitational field strength g at the surface of a spherical planet of uniform density is given by

g=\frac{G M}{R^{2}}

where M is the mass of the planet, R is its radius and G is the gravitational constant. You can assume that spherical objects of uniform density act as point masses.

[ 2 ]

(c)

The gravitational field strength at the surface of Mars $g_{\mathrm{M}}$ is related to the gravitational field strength at the surface of the Earth $g_{\mathrm{E}}$ by

g_{\mathrm{M}}=0.38 \times g_{\mathrm{E}}

The radius of Mars $R_{\mathrm{M}}$ is related to the radius of the Earth $R_{\mathrm{E}}$ by

R_{\mathrm{M}}=0.53 \times R_{\mathrm{E}}

Determine the mass of Mars $M_{\mathrm{M}}$ in terms of the mass of the Earth $M_{\mathrm{E}}$ .

[ 2 ]

(d)

On the diagram below, draw lines to represent the gravitational field around the planet Mars.
Mars

[ 1 ]

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Covered syllabus points

D. Fields question 1

D. Fields question 2

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)

D. Fields question 3

Question (a)

Question (b)

Question (c)

D. Fields question 4

Question (a)

Question (b)

Question (c)

Question (d)