IB Physics SL Theme D: Fields questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

Type

Multiple choice Written

Difficulty

Easy Medium Hard

Question 1

Paper 2Medium12 marks

A probe is outside a spherical asteroid of uniform density. The asteroid has radius $4.0\times10^5\ \mathrm{m}$ The probe has mass $800\ \mathrm{kg}$ Figure 1 shows the meaning of $r$ and measured values of the gravitational force $F$ on the probe at different distances from the asteroid’s centre.

The gravitational constant is $G=6.67\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$

(a)

State how the asteroid’s mass is treated when calculating the gravitational force on the probe.

[1]

(b)

Use Figure 1 to state the measured gravitational force when $r=6.0\times10^5\ \mathrm{m}$

[1]

(c)

Use this measurement to estimate the mass of the asteroid.

[3]

(d)

Using your estimate from (c), calculate the gravitational force on the $800\ \mathrm{kg}$ probe when $r=8.0\times10^5\ \mathrm{m}$ State whether this result agrees with Figure 1.

[3]

(e)

At $r=8.0\times10^5\ \mathrm{m}$ a second probe has a mass of $1.6\times10^3\ \mathrm{kg}$ Determine the gravitational force on this probe.

[2]

(f)

A student suggests that the readings at $r=6.0\times10^5\ \mathrm{m}$ and $r=8.0\times10^5\ \mathrm{m}$ are consistent with $F\propto 1/r$ Use these readings to assess the suggestion.

[2]

Question 2

Multiple choiceHard1 mark

A satellite moves in an elliptical orbit around a planet. Its closest and farthest distances from the planet are $1.0\times10^7\text{ m}$ and $7.0\times10^7\text{ m}$ A satellite in a circular orbit around the same planet has radius $2.0\times10^7\text{ m}$ and period $4.0\text{ d}$ Which pair gives the elliptical orbit’s period, followed by the ratio of its speed at closest approach to its speed at farthest distance?

Show answer and explanation

Answer: C. For the same planet, Kepler’s third law gives $T^2/a^3=\text{constant}$ and Kepler’s second law gives equal swept areas in equal times.

The semi-major axis is $a=(1.0+7.0)\times10^7/2=4.0\times10^7\text{ m}$ Thus $T=4.0(4.0/2.0)^{3/2}=11.3\text{ d}$ which rounds to $11\text{ d}$
At closest and farthest approach, velocity is perpendicular to the radius, so equal area rates give $r_{\rm close}v_{\rm close}=r_{\rm far}v_{\rm far}$ Hence $v_{\rm close}/v_{\rm far}=7$ A: omits the cube in Kepler’s third-law relation, using $T/T_0=\sqrt{a/a_0}$ B: reverses the speed ratio. D: uses $T/T_0=(a/a_0)^3$ omitting the square root. Remember: orbital speed is greater nearer the central body.

Question 3

Paper 2Medium4 marks

During a Millikan-type investigation, the charge magnitudes of positively charged oil droplets are measured. Droplets A and B coalesce to form droplet C. No charge is transferred to or from the surroundings during coalescence. Figure 1 also shows measurements for droplets D and E. Each plotted measurement has an uncertainty of ±0.1 in the units shown.

(a)

Use Figure 1 to estimate the elementary charge and explain how the measurements provide evidence that electric charge is quantized.

[2]

(b)

Using your estimate in (a), assess whether the coalescence of A and B is consistent with conservation of electric charge.

[2]

Question 4

Multiple choiceHard1 mark

Two oil drops P and R have initial charges $+18Q$ and $-10Q$ where $Q>0$ They exchange charge in isolation, and afterward P has charge $+14Q$ Treat all readings as exact; $e$ is the greatest positive unit of which every initial and final charge is an integer multiple. Which pair gives $q_{R,\mathrm f}$ and the number of elementary-charge units transferred? [1]

Show answer and explanation

Answer: A [1]. The total charge of the isolated pair is conserved, and each drop’s charge is an integer multiple of $e$ The initial total is $(18-10)Q=+8Q$ so $q_{R,\mathrm f}=+8Q-14Q=-6Q$ The charge magnitudes $18Q, 10Q, 14Q$ and $6Q$ have greatest common unit $e=2Q$ P’s charge changes by $4Q$ so $4Q/(2Q)=2$ elementary-charge units are transferred.

B: uses $Q$ rather than the greatest common unit $2Q$ as $e$
C: gives the residual charge the wrong sign.
D: assigns R the same signed change as P, rather than the opposite change required by conservation.

Remember: in an isolated pair, the signed charge changes sum to zero.

Total: 1 mark.

Question 5

Multiple choiceMedium1 mark

Particles X and Y, each with charge magnitude $q$ enter the same uniform magnetic field at right angles to the field with equal speeds. Only magnetic forces act. Each follows a semicircular path, and Y’s path radius is twice X’s. Which row gives the ratios $(|q|/m)_Y/(|q|/m)_X$ and $K_Y/K_X$ respectively, after both particles complete their semicircles?

Show answer and explanation

Answer: B. The magnetic force supplies the centripetal force, so $|q|vB=mv^2/r$ giving $|q|/m=v/(Br)$ With equal speeds and the same field, the charge-to-mass ratio is inversely proportional to radius, so the ratio for Y and X is $1/2$ Equal charge magnitudes then give $m_Y/m_X=2$ and equal speeds give $K_Y/K_X=2$ The magnetic force is perpendicular to the motion, so neither particle’s kinetic energy changes during its semicircle.

A: Gets the charge-to-mass ratio right but assumes equal speeds mean equal kinetic energies, overlooking the different masses.
C: Treats charge-to-mass ratio as directly proportional to radius; this also gives the inverse mass and kinetic-energy ratio.
D: Reverses the charge-to-mass ratio’s dependence on radius but correctly uses $K\propto m$ at equal speed.
Remember: a magnetic force changes a particle’s direction, not its kinetic energy.

Question 6

Paper 2Medium8 marks

An electron enters the region between two parallel plates as shown in Figure 1. The electric field between the plates is uniform. Ignore edge effects and the gravitational force on the electron. The electron has no initial vertical velocity.

The magnitude of the electron’s charge is $1.60\times10^{-19}\ \mathrm{C}$ and its mass is $9.11\times10^{-31}\ \mathrm{kg}$

(a)

State the direction of the electric force on the electron.

[1]

(b)

Calculate the magnitude of the electric field between the plates.

[1]

(c)

Calculate the magnitude of the electron’s acceleration between the plates.

[2]

(d)

Determine the vertical displacement of the electron from its entry point when it reaches the right end of the plates.

[3]

(e)

Determine the vertical component of the electron’s velocity at the instant it reaches the right end of the plates.

[1]

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