20.3. Force on a moving charge
A subsection of Physics, 9702, through 20. Magnetic fields
Listing 10 of 105 questions
Define magnetic flux density. Electrons are moving in a vacuum with speed 1.7 × 107 m s–1. The electrons enter a uniform magnetic field of flux density 4.8 mT. shows the path of the electrons. d X electrons, speed 1.7 × 107 m s–1 magnetic field, flux density 4.8 mT The path of the electrons remains in the plane of the page. State the direction of the magnetic field. Show that the magnitude of the force exerted on each electron by the magnetic field is 1.3 × 10–14 N. On , draw an arrow to indicate the direction of the centripetal acceleration of the electron where it enters the magnetic field at point X. Use the information in to calculate the distance d between the path of the electrons entering the magnetic field and the path of the electrons leaving it. d = m The electrons in are replaced with positrons that are moving with speed 3.4 × 107 m s–1 along the same initial path as the electrons. The positrons enter the magnetic field at point X on . On , draw a line to show the path of the positrons through the magnetic field.
9702_w23_qp_41
THEORY
2023
Paper 4, Variant 1
View
Define magnetic flux density. Electrons are moving in a vacuum with speed 1.7 × 107 m s–1. The electrons enter a uniform magnetic field of flux density 4.8 mT. shows the path of the electrons. d X electrons, speed 1.7 × 107 m s–1 magnetic field, flux density 4.8 mT The path of the electrons remains in the plane of the page. State the direction of the magnetic field. Show that the magnitude of the force exerted on each electron by the magnetic field is 1.3 × 10–14 N. On , draw an arrow to indicate the direction of the centripetal acceleration of the electron where it enters the magnetic field at point X. Use the information in to calculate the distance d between the path of the electrons entering the magnetic field and the path of the electrons leaving it. d = m The electrons in are replaced with positrons that are moving with speed 3.4 × 107 m s–1 along the same initial path as the electrons. The positrons enter the magnetic field at point X on . On , draw a line to show the path of the positrons through the magnetic field.
9702_w23_qp_43
THEORY
2023
Paper 4, Variant 3
View
A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density B, as shown in . Q R X Y V P S W direction of motion of electrons magnetic field flux density B Electrons enter the slice at right-angles to face SRXY. A potential difference, the Hall voltage VH, is developed between two faces of the slice. Use letters from to name the two faces between which the Hall voltage is developed. and State and explain which of the two faces named in is the more positive. The Hall voltage VH is given by the expression VH = BI ntq. Use the letters in to identify the distance t. State the meaning of the symbol n. State and explain the effect, if any, on the polarity of the Hall voltage when negative charge carriers are replaced with positive charge carriers, moving in the same direction towards the slice.
9702_m18_qp_42
THEORY
2018
Paper 4, Variant 2
View
A Hall probe is placed in a magnetic field. The Hall voltage is zero. The Hall probe is rotated to a new position in the magnetic field. The Hall voltage is now maximum. Explain these observations. The formula for calculating the Hall voltage VH as measured by a Hall probe is VH = BI ntq. Table 6.1 shows the value of n for two materials. Table 6.1 material n / m–3 silicon 9.65 × 1015 copper 8.49 × 1028 State the meaning of n. Explain why a Hall probe is made from silicon rather than copper. A Hall probe gives a maximum reading of 24 mV when placed in a uniform magnetic field of flux density 32 mT. The same Hall probe is then placed in a magnetic field of fixed direction and varying flux density. The Hall probe is in a fixed position so that the angle between the Hall probe and the magnetic field is the same as when the Hall voltage was 24 mV. The variation of the reading VH on the Hall probe with time t from time t = 0 to time t = 8.6 s is shown in . t / s VH / mV A coil with 780 turns and a diameter of 3.6 cm is placed in this varying magnetic field. The plane of the coil is perpendicular to the field lines. Calculate the magnitude of the maximum electromotive force (e.m.f.) induced in the coil in the time between t = 0 and t = 8.6 s. e.m.f. = V
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
View
A solenoid is connected in series with a battery and a switch. A Hall probe is placed close to one end of the solenoid, as illustrated in . solenoid Hall probe The current in the solenoid is switched on. The Hall probe is adjusted in position to give the maximum reading. The current is then switched off. The current in the solenoid is now switched on again. Several seconds later, it is switched off. The Hall probe is not moved. On the axes of , sketch a graph to show the variation with time t of the Hall voltage VH. VH current switched on current switched off t The Hall probe is now replaced by a small coil. The plane of the coil is parallel to the end of the solenoid. State Faraday’s law of electromagnetic induction. On the axes of , sketch a graph to show the variation with time t of the e.m.f. E induced in the coil when the current in the solenoid is switched on and then switched off. E current switched on current switched off t
9702_s14_qp_41
THEORY
2014
Paper 4, Variant 1
View
A Hall probe is placed a distance d from a long straight current-carrying wire, as illustrated in . Hall probe current-carrying wire 4.0 A X Y d The direct current in the wire is 4.0 A. Line XY is normal to the wire. The Hall probe is rotated about the line XY to the position where the reading VH of the Hall probe is maximum. The Hall probe is now moved away from the wire, along the line XY. On the axes of , sketch a graph to show the variation of the Hall voltage VH with distance x of the probe from the wire. Numerical values are not required on your sketch. VH x d The Hall probe is now returned to its original position, a distance d from the wire. At this point, the magnetic flux density due to the current in the wire is proportional to the current. For a direct current of 4.0 A in the wire, the reading of the Hall probe is 3.5 mV. The direct current is now replaced by an alternating current of root-mean-square (r.m.s.) value 4.0 A. The period of this alternating current is T. On the axes of , sketch the variation with time t of the reading of the Hall voltage VH for two cycles of the alternating current. Give numerical values for VH, where appropriate. VH / mV t T 2T –6 –4 –2 A student suggests that the Hall probe in is replaced with a small coil connected in series with a millivoltmeter. The constant current in the wire is 4.0 A. In order to obtain data to plot a graph showing the variation with distance x of the magnetic flux density, the student suggests that readings of the millivoltmeter are taken when the coil is held in position at different values of x. Comment on this suggestion.
9702_s14_qp_42
THEORY
2014
Paper 4, Variant 2
View
A solenoid is connected in series with a battery and a switch. A Hall probe is placed close to one end of the solenoid, as illustrated in . solenoid Hall probe The current in the solenoid is switched on. The Hall probe is adjusted in position to give the maximum reading. The current is then switched off. The current in the solenoid is now switched on again. Several seconds later, it is switched off. The Hall probe is not moved. On the axes of , sketch a graph to show the variation with time t of the Hall voltage VH. VH current switched on current switched off t The Hall probe is now replaced by a small coil. The plane of the coil is parallel to the end of the solenoid. State Faraday’s law of electromagnetic induction. On the axes of , sketch a graph to show the variation with time t of the e.m.f. E induced in the coil when the current in the solenoid is switched on and then switched off. E current switched on current switched off t
9702_s14_qp_43
THEORY
2014
Paper 4, Variant 3
View
A thin rectangular slice of aluminium has sides of length 65 mm, 50 mm and 0.10 mm, as shown in . current direction of magnetic field 3.8 A 0.10 mm 50 mm 65 mm P Q Z Y X R S (not to scale) Some of the corners of the slice are labelled. A current I of 3.8 A is normal to face RSXY of the slice. In aluminium, the number of free electrons per unit volume is 6.0 × 1028 m−3. A uniform magnetic field of magnetic flux density B equal to 0.13 T is normal to face QRYZ of the aluminium slice in the direction from Q to P. A Hall voltage VH is developed across the slice and is given by the expression VH = BI ntq . Use to state the magnitude of the distance t. t = mm Calculate the magnitude of the Hall voltage VH. VH = V
9702_s16_qp_41
THEORY
2016
Paper 4, Variant 1
View
A magnetic field of flux density B is normal to face PQRS of a slice of a conducting material, as shown in . P X Q Y R S Z magnetic field flux density % FXUUHQWI A current I in the slice is normal to face QRZY of the slice. The Hall voltage VH across the slice is given by the expression VH = BI ntq . State what is represented by the symbol n. The symbol t represents the length of one side of the slice. Use letters from to identify t. In general, the Hall voltage produced in a slice of a metal is very small. For a slice of the same dimensions with the same current and magnetic flux density, the Hall voltage produced in a semiconductor material is much larger. Suggest and explain why. In some semiconducting materials, electrons are mainly responsible for conduction. In other semiconducting materials, holes are mainly responsible for conduction. Suggest and explain the difference, if any, that conduction by electrons or by holes will have on the Hall voltage.
9702_s16_qp_42
THEORY
2016
Paper 4, Variant 2
View
A thin rectangular slice of aluminium has sides of length 65 mm, 50 mm and 0.10 mm, as shown in . current direction of magnetic field 3.8 A 0.10 mm 50 mm 65 mm P Q Z Y X R S (not to scale) Some of the corners of the slice are labelled. A current I of 3.8 A is normal to face RSXY of the slice. In aluminium, the number of free electrons per unit volume is 6.0 × 1028 m−3. A uniform magnetic field of magnetic flux density B equal to 0.13 T is normal to face QRYZ of the aluminium slice in the direction from Q to P. A Hall voltage VH is developed across the slice and is given by the expression VH = BI ntq . Use to state the magnitude of the distance t. t = mm Calculate the magnitude of the Hall voltage VH. VH = V
9702_s16_qp_43
THEORY
2016
Paper 4, Variant 3
View
Questions Discovered
105