IB Physics SL D: 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 ]

[Maximum number: 8]

(a)

Define electric field strength.

[ 2 ]

(b)

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

[ 4 ]

(i)

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

[ 2 ]

(ii)

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.

[ 2 ]

(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 $F=\frac{\left(1.60 \times 10^{-19}\right)^{2}}{\left(5.0 \times 10^{-3}\right)^{2}} \times 8.99 \times 10^{9}$ ;
$9.2 \times 10^{-24} \mathrm{~N} ;$

[Maximum number: 5]

(a)

The diagram shows a junction in a circuit.

The currents in the three wires are related by $I_{1}=I_{2}+I_{3}$ .
State the fundamental law of Physics from which this relation is derived.

[ 1 ]

(b)

A proton moves on a circular path in a region of uniform magnetic field of magnetic flux density B that is directed into the plane of the page.

[ 4 ]

(i)

On the diagram, draw an arrow to indicate the velocity of the proton at the position shown.

[ 1 ]

(ii)

Show that the frequency of revolution of the proton is given by $f=\frac{e B}{2 \pi m_{\mathrm{p}}}$ .

[ 3 ]

$\begin{aligned} e v B=\frac{m_{\mathrm{p}} v^{2}}{R} f=\frac{1}{T}=\frac{v}{2 \pi R} \end{aligned}$

Both q and e are acceptable for the
charge.

[3]

Algebra leading to required expression $\boldsymbol{<}=\frac{e B}{2 \pi m_{\mathrm{p}}} \boldsymbol{} \boldsymbol{}$

IB Physics SL D: Fields Question Bank

Covered syllabus points

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)

D. Fields question 5

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

D. Fields question 6

Question (a)

Question (b)

Question (i)

Question (ii)