SL Paper 2
A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.
The charge per unit area on the surface of the wall is σ. It can be shown that the electric field strength E due to the charge on the wall is given by the equation
.
Demonstrate that the units of the quantities in this equation are consistent.
The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.
Determine the horizontal force that acts on the ball.
The charge on the ball is 1.2 × 10−6 C. Determine σ.
The centre of the ball, still carrying a charge of , is now placed from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.
P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is .
Calculate the charge on Q. State your answer to an appropriate number of significant figures.
A charged particle, P, of charge +68 μC is fixed in space. A second particle, Q, of charge +0.25 μC is held at a distance of 48 cm from P and is then released.
The diagram shows two parallel wires X and Y that carry equal currents into the page.
Point Q is equidistant from the two wires. The magnetic field at Q due to wire X alone is 15 mT.
The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.
Determine the force on Q at the instant it is released.
Describe the motion of Q after release.
On the diagram draw an arrow to show the direction of the magnetic field at Q due to wire X alone.
Determine the magnitude and direction of the resultant magnetic field at Q.
The graph shows how current I varies with potential difference V for a resistor R and a non-ohmic component T.
(i) State how the resistance of T varies with the current going through T.
(ii) Deduce, without a numerical calculation, whether R or T has the greater resistance at I=0.40 A.
Components R and T are placed in a circuit. Both meters are ideal.
Slider Z of the potentiometer is moved from Y to X.
(i) State what happens to the magnitude of the current in the ammeter.
(ii) Estimate, with an explanation, the voltmeter reading when the ammeter reads 0.20 A.
A lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.
The following data are available for the lamps when at their working temperature.
Lamp specifications 24 V, 5.0 W
Power supply emf 24 V
Power supply maximum current 8.0 A
Length of each rod 12.5 m
Resistivity of rod metal 7.2 × 10–7 Ω m
Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.
Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.
One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline one other electrical advantage of this system compared to one in which the lamps are connected in series.
A possible decay of a lambda particle () is shown by the Feynman diagram.
State the quark structures of a meson and a baryon.
Explain which interaction is responsible for this decay.
Draw arrow heads on the lines representing and d in the .
Identify the exchange particle in this decay.
Outline one benefit of international cooperation in the construction or use of high-energy particle accelerators.
A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable.
The following data are available:
Length of cable = 10 m
Cross-sectional area of cable = 6.0 mm2
Resistivity of copper = 1.7 × 10–8 Ω m
Calculate the current in the copper cable.
Calculate the resistance of the cable.
Explain, in terms of electrons, what happens to the resistance of the cable as the temperature of the cable increases.
The heater changes the temperature of the water by 35 K. The specific heat capacity of water is 4200 J kg–1 K–1.
Determine the rate at which water flows through the shower. State an appropriate unit for your answer.
The graph shows how current varies with potential difference across a component X.
Component X and a cell of negligible internal resistance are placed in a circuit.
A variable resistor R is connected in series with component X. The ammeter reads .
Component X and the cell are now placed in a potential divider circuit.
Outline why component X is considered non-ohmic.
Determine the resistance of the variable resistor.
Calculate the power dissipated in the circuit.
State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.
Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).
Electrical resistors can be made by forming a thin film of carbon on a layer of an insulating material.
A carbon film resistor is made from a film of width 8.0 mm and of thickness 2.0 μm. The diagram shows the direction of charge flow through the resistor.
The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10–5 Ω m. Calculate the length l of the film.
The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.
State why knowledge of quantities such as resistivity is useful to scientists.
The current direction is now changed so that charge flows vertically through the film.
Deduce, without calculation, the change in the resistance.
Draw a circuit diagram to show how you could measure the resistance of the carbon-film resistor using a potential divider arrangement to limit the potential difference across the resistor.
A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.
A mass of 0.86 kg of water remains after it has boiled for 200 s.
The electric heater has two identical resistors connected in parallel.
The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.
The molar mass of water is 18 g mol−1. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.
State one assumption of the kinetic model of an ideal gas.
Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.
Explain why the temperature of water remains at 100 °C during this time.
The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.
Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.
Specific heat capacity of pasta = 1.8 kJ kg−1 K−1
Specific heat capacity of water = 4.2 kJ kg−1 K−1
Show that each resistor has a resistance of about 30 Ω.
Calculate the power transferred by the heater when both switches are closed.
An electron moves in circular motion in a uniform magnetic field.
The velocity of the electron at point P is 6.8 × 105 m s–1 in the direction shown.
The magnitude of the magnetic field is 8.5 T.
State the direction of the magnetic field.
Calculate, in N, the magnitude of the magnetic force acting on the electron.
Explain why the electron moves at constant speed.
Explain why the electron moves on a circular path.
An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.
The following data are available for the conductor:
density of free electrons = 8.5 × 1022 cm−3
resistivity ρ = 1.7 × 10−8 Ωm
dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.
The ammeter reading is 2.0 A.
Calculate the resistance of the conductor.
Calculate the drift speed v of the electrons in the conductor in cm s–1. State your answer to an appropriate number of significant figures.
The diagram shows a potential divider circuit used to measure the emf E of a cell X. Both cells have negligible internal resistance.
AB is a wire of uniform cross-section and length 1.0 m. The resistance of wire AB is 80 Ω. When the length of AC is 0.35 m the current in cell X is zero.
State what is meant by the emf of a cell.
Show that the resistance of the wire AC is 28 Ω.
Determine E.
A proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.
Label with arrows on the diagram the magnetic force F on the proton.
Label with arrows on the velocity vector v of the proton.
The speed of the proton is 2.16 × 106 m s-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.
A proton is moving in a region of uniform magnetic field. The magnetic field is directed into the plane of the paper. The arrow shows the velocity of the proton at one instant and the dotted circle gives the path followed by the proton.
The speed of the proton is 2.0 × 106 m s–1 and the magnetic field strength B is 0.35 T.
Explain why the path of the proton is a circle.
Show that the radius of the path is about 6 cm.
Calculate the time for one complete revolution.
Explain why the kinetic energy of the proton is constant.
An electron is placed at a distance of 0.40 m from a fixed point charge of –6.0 mC.
Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 108 N C–1.
Calculate the magnitude of the initial acceleration of the electron.
Describe the subsequent motion of the electron.
The cable consists of 32 copper wires each of length 35 km. Each wire has a resistance of 64 Ω. The resistivity of copper is 1.7 x 10–8 Ω m.
A cable consisting of many copper wires is used to transfer electrical energy from a generator to an electrical load. The copper wires are protected by an insulator.
The copper wires and insulator are both exposed to an electric field. Discuss, with reference to charge carriers, why there is a significant electric current only in the copper wires.
Calculate the radius of each wire.
There is a current of 730 A in the cable. Show that the power loss in 1 m of the cable is about 30 W.
When the current is switched on in the cable the initial rate of rise of temperature of the cable is 35 mK s–1. The specific heat capacity of copper is 390 J kg–1 K–1. Determine the mass of a length of one metre of the cable.
A power supply is connected to three resistors P, Q and R of fixed value and to an ideal voltmeter. A variable resistor S, formed from a solid cylinder of conducting putty, is also connected in the circuit. Conducting putty is a material that can be moulded so that the resistance of S can be changed by re-shaping it.
The resistance values of P, Q and R are 40 Ω, 16 Ω and 60 Ω respectively. The emf of the power supply is 6.0 V and its internal resistance is negligible.
All the putty is reshaped into a solid cylinder that is four times longer than the original length.
Calculate the potential difference across P.
The voltmeter reads zero. Determine the resistance of S.
Deduce the resistance of this new cylinder when it has been reshaped.
Outline, without calculation, the change in the total power dissipated in Q and the new cylinder after it has been reshaped.
A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.
When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.
Electricity can be generated using renewable resources.
Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.
State the emf of the cell.
Deduce the internal resistance of the cell.
The voltmeter is used in another circuit that contains two secondary cells.
Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.
Calculate the reading on the voltmeter.
Outline why electricity is a secondary energy source.
Some fuel sources are renewable. Outline what is meant by renewable.
A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.
The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m−2.
The overall efficiency of the re-charging process is 18 %.
Calculate the minimum time required to re-charge the cell fully.
Outline why research into solar cell technology is important to society.
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.
The mass of ions ejected each second is 6.6 × 10–6 kg and the speed of each ion is 5.2 × 104 m 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.
An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.
In practice, the ions leave the spacecraft at a range of angles as shown.
On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.
Determine the initial acceleration of the spacecraft.
Estimate the maximum speed of the spacecraft.
Outline why scientists sometimes use estimates in making calculations.
Outline why the ions are likely to spread out.
Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.
Outline what is meant by the gravitational field strength at a point.
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.
Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.
The switch S is initially open. Calculate the total power dissipated in the circuit.
The switch is now closed. State, without calculation, why the current in the cell will increase.
The switch is now closed. Deduce the ratio .
A photovoltaic cell is supplying energy to an external circuit. The photovoltaic cell can be modelled as a practical electrical cell with internal resistance.
The intensity of solar radiation incident on the photovoltaic cell at a particular time is at a maximum for the place where the cell is positioned.
The following data are available for this particular time:
Operating current = 0.90 A
Output potential difference to external circuit = 14.5 V
Output emf of photovoltaic cell = 21.0 V
Area of panel = 350 mm × 450 mm
Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.
Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.
The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m−2.
A measure of the efficiency of a photovoltaic cell is the ratio
Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.
State two reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.
A girl rides a bicycle that is powered by an electric motor. A battery transfers energy to the electric motor. The emf of the battery is 16 V and it can deliver a charge of 43 kC when discharging completely from a full charge.
The maximum speed of the girl on a horizontal road is 7.0 m s–1 with energy from the battery alone. The maximum distance that the girl can travel under these conditions is 20 km.
The bicycle and the girl have a total mass of 66 kg. The girl rides up a slope that is at an angle of 3.0° to the horizontal.
The bicycle has a meter that displays the current and the terminal potential difference (pd) for the battery when the motor is running. The diagram shows the meter readings at one instant. The emf of the cell is 16 V.
The battery is made from an arrangement of 10 identical cells as shown.
Show that the time taken for the battery to discharge is about 3 × 103 s.
Deduce that the average power output of the battery is about 240 W.
Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.
Calculate the component of weight for the bicycle and girl acting down the slope.
The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).
Calculate the maximum speed of the bicycle and the girl up the slope.
On another journey up the slope, the girl carries an additional mass. Explain whether carrying this mass will change the maximum distance that the bicycle can travel along the slope.
Determine the internal resistance of the battery.
Calculate the emf of one cell.
Calculate the internal resistance of one cell.