D.3 Motion in electromagnetic fields: IB Physics SL exam-style questions

A straight wire of length 0.40 m carries a current of 3.0 A at right angles to a uniform magnetic field of flux density 0.25 T.

What is the force on the wire?

A straight wire carrying a current lies at 30° to a uniform magnetic field. The magnetic force on the wire is F.

The wire is turned until it is at right angles to the field. The current and the length of wire in the field do not change. What is the magnetic force on the wire now?

A proton and an alpha particle move at right angles to the same uniform magnetic field. The speed of the alpha particle is one quarter of the speed of the proton.

What is (magnetic force on the alpha particle)/(magnetic force on the proton)?

A particle of charge q and mass m moves with speed v at right angles to a uniform magnetic field of flux density B. It follows a circular path of radius r.

Which expression gives the charge-to-mass ratio q/m of the particle?

A straight wire in the plane of the page carries a current towards the bottom of the page. A uniform magnetic field is directed out of the page.

What is the direction of the magnetic force on the wire?

Two long parallel wires 0.10 m apart in a vacuum carry currents of 5.0 A and 3.0 A in the same direction.

Which row gives the magnitude of the force per unit length on each wire and describes the force?

A proton is released from rest in a uniform electric field in a vacuum.

Which graph shows the variation of the kinetic energy E_k of the proton with the distance s it has moved?

A student investigates the force on a current-carrying conductor. Two flat magnets are fixed to a steel yoke that rests on a top-pan balance of resolution 0.01 g. Seen from above, the north pole is on the student's left and the south pole on the student's right. A stiff copper rod is clamped horizontally so that it runs directly away from the student through the gap between the poles, without touching the magnets. The length of rod in the field is equal to the length of the pole faces, (5.0 ± 0.1) cm.

When there is a current I in the rod, the balance reading decreases by Δm. The uncertainty in each value of Δm is ±0.02 g.

A horizontal copper rod of mass (4.80 ± 0.01) g hangs from two light vertical conducting wires, forming a swing. A pair of large coils produces a uniform vertical magnetic field of flux density B in the region of the rod. The length of the rod between the two suspension wires is (0.120 ± 0.001) m.

When there is a current I in the rod it swings sideways and comes to rest with the suspension wires at an angle φ to the vertical, measured with a protractor to ±1°. In equilibrium, tan φ = BIL/(mg), where m is the mass and L the length of the rod. The graph shows tan φ against I with error bars.

A student uses a fine-beam tube to determine the charge-to-mass ratio e/m of the electron. Electrons are accelerated from rest through a potential difference V and then move at right angles to a uniform magnetic field produced by a pair of coils. The flux density is (8.0 ± 0.2) × 10⁻⁴ T and is kept constant. The electrons follow a circular path, made visible by the gas in the tube.

The student holds a ruler against the front of the glass bulb and, looking from the front, reads the diameter D of the circle to ±0.2 cm. The table gives r = D/2 and r²; the graph shows r² against V with error bars.

A student uses a current balance to determine the magnetic constant μ₀. A straight horizontal brass rod rests on an insulating block on a top-pan balance of resolution 0.001 g. An identical rod is clamped directly above it, parallel to it. The two rods are connected in series so that the same current I flows through each, in opposite directions. The length of each rod is (0.300 ± 0.002) m and the separation of their centres is (5.0 ± 0.2) mm.

For each current the student records the increase Δm in the balance reading with the current in one direction, then reverses the current and records it again. The table gives the mean of the two values, with an uncertainty of ±0.002 g. The graph shows Δm against I² with error bars.

In an electron deflection tube, electrons accelerated through a potential difference V_a = (3.00 ± 0.05) kV enter the region between two horizontal parallel plates, travelling horizontally midway between them. The plates are (50.0 ± 0.5) mm apart and the upper plate is at a potential difference V_p = (1.20 ± 0.02) kV above the lower plate.

The path of the beam is shown on a fluorescent screen marked with a grid. A student reads the upward deflection y of the beam at horizontal distances x from the point where the beam enters the field. Each value of y has an uncertainty of ±1 mm. Theory predicts y = kx², where k = V_p/(4dV_a) and d is the plate separation.

Polonium-210 (²¹⁰₈₄Po) decays by emitting alpha particles, all with a kinetic energy of 5.30 MeV.

In an evacuated chamber, a narrow beam of these alpha particles moving to the right enters a large region of uniform magnetic field of flux density 1.50 T, directed into the page.

Mass of an alpha particle = 6.64 × 10⁻²⁷ kg. Charge of an alpha particle = +3.20 × 10⁻¹⁹ C.

A model electromagnetic launcher has two horizontal parallel metal rails 0.080 m apart. A metal rod rests across the rails and is fixed to a light trolley. The total mass of the rod and trolley is 0.150 kg. A uniform vertical magnetic field of flux density 0.25 T acts over the whole length of the rails.

A supply drives a constant current of 12 A through the rails and the rod. The diagram shows the arrangement seen from above.

In an ion-beam laboratory, positive ions from an ion source are accelerated from rest through a potential difference of 46.7 kV. They then travel along an evacuated beam line, as shown. Two detectors, D₁ and D₂, 2.40 m apart, record each ion as it passes. The time between the two signals is 1.60 μs.

At X the ions enter a bending magnet, a region of uniform magnetic field perpendicular to the page. Inside the magnet the ions follow a quarter circle of radius 0.250 m and leave towards the target.

In an ion implanter used in making computer chips, singly charged boron ions, each of charge +1.60 × 10⁻¹⁹ C, are accelerated from rest through a potential difference of 20.0 kV. They then enter a velocity filter: two horizontal parallel plates 20.0 mm apart, with a uniform magnetic field of flux density 0.0500 T directed into the page between them.

The filter is set so that boron-11 ions, of mass 1.83 × 10⁻²⁶ kg, pass straight through. Boron-10 ions have a mass of 1.66 × 10⁻²⁶ kg.

In an aluminium smelter, very large direct currents are carried by long, straight, parallel metal bars called bus bars. Two bus bars P and Q are 0.12 m apart. P carries a current of 3.0 kA into the page and Q carries a current of 3.0 kA out of the page, as shown in the cross-section.

A space probe is driven by an ion engine. Xenon ions, each of mass 2.18 × 10⁻²⁵ kg and charge +1.60 × 10⁻¹⁹ C, start almost at rest at grid P. A uniform electric field accelerates them to grid Q, which is 1.20 mm from P. The potential difference between the grids is 1100 V.

The ions leave the engine as a beam. The current in the beam is 1.40 A.

An electron enters the uniform electric field between two parallel plates, moving parallel to the plates. It leaves the plates with a deflection y.

The potential difference between the plates is doubled and the entry speed of the electron is doubled. The electron still leaves the plates. What is (new deflection)/y?

A proton and an electron travel at the same speed at right angles to the same uniform magnetic field.

What is (radius of the path of the proton)/(radius of the path of the electron)?

In a velocity selector the electric field strength is 4.5 × 10⁴ V m⁻¹ and the magnetic flux density is 0.030 T. The diagram shows the electric and magnetic forces on a negatively charged particle moving through the selector.

What speed must the particle have to pass through undeflected?

A positive ion enters a region of uniform field moving at right angles to the field lines. In one experiment the field is electric; in another it is magnetic.

Which row describes the path of the ion while it is in each field?

Two long parallel wires X and Y carry currents I and 3I respectively.

What is (force per unit length on Y)/(force per unit length on X)?

An electron moves from left to right across the page. A uniform magnetic field is directed into the page.

What is the direction of the magnetic force on the electron as it enters the field?

The diagram shows a positive ion moving in a circle in a uniform magnetic field directed into the page.

Which row describes the kinetic energy and the momentum of the ion as it moves round the circle?

In a deflection tube, electrons accelerated from rest through a potential difference V_a travel from left to right across the page, midway between two horizontal parallel plates (50.0 ± 0.5) mm apart. The upper plate is positive. A pair of coils produces a uniform magnetic field of flux density (1.20 ± 0.02) mT, perpendicular to the page, in the region between the plates.

For each value of V_a (uncertainty ±0.05 kV), the student adjusts the potential difference V_p between the plates until the beam passes through undeflected. Judging this gives an uncertainty in V_p of ±20 V. The student tests whether V_p = cV_aⁿ, where c and n are constants, by plotting lg (V_p / V) against lg (V_a / V). Four points have been plotted.

A student uses a computer simulation of a mass spectrometer. Singly charged positive ions, initially at rest, are accelerated through a potential difference of 2.00 kV and then enter a uniform magnetic field of flux density 0.250 T at right angles to the field. Each ion travels through a semicircle and strikes a detector. The student measures the diameter D of each semicircle with the simulation's on-screen ruler, to ±1 mm.

The masses m of the ions, in unified atomic mass units (u), are taken from a published table of isotope masses. The student plots lg (D / mm) against lg (m / u); five points have been plotted.

A straight horizontal wire of length (40.0 ± 0.5) mm lies between the wide, flat pole pieces of an electromagnet, where the magnetic field is uniform and horizontal. The wire is fixed to a holder on a force sensor and can be turned in the horizontal plane so that it makes an angle θ with the field; the leads to the wire are twisted together outside the field.

The current in the wire is kept at (2.00 ± 0.01) A. The sensor measures the vertical force F on the wire with an uncertainty of ±0.2 mN.

In an ion-energy analyser, two parallel wire-mesh grids G1 and G2 are 12.0 mm apart in a vacuum. Protons, each with a kinetic energy of 450 eV, pass through G1 moving at right angles to the grids, towards G2 (Figure 1). A potential difference V is applied between the grids so that G2 is positive relative to G1. The field between the grids is uniform.

e = 1.60 × 10⁻¹⁹ C; mass of a proton = 1.67 × 10⁻²⁷ kg.

In a moving-coil loudspeaker, a coil of 60 turns, each of radius 12 mm, sits in the narrow gap of a magnet. The magnetic field in the gap is radial, with flux density 0.80 T, so the field is perpendicular to the wire at every point. The coil is fixed to a cone; together they have a mass of 8.0 g. The suspension of the cone behaves as a spring of spring constant 1.6 × 10³ N m⁻¹.

The diagram shows a cross-section through the axis of the coil. In the coil, the current is out of the page at the top and into the page at the bottom; the field points away from the axis.

Electrons are accelerated from rest through a potential difference of 2.0 kV. They then enter, at right angles to its boundary, a region of uniform magnetic field of flux density 1.5 mT directed into the page. The field region has two parallel boundaries 50 mm apart and extends far above and below the beam.

e = 1.60 × 10⁻¹⁹ C; m_e = 9.11 × 10⁻³¹ kg.

Three long, straight, parallel cables X, Y and Z lie in a row on a horizontal cable tray. The diagram shows a cross-section. X carries a current of 200 A and Y carries 150 A, both out of the page; Z carries 300 A into the page. The distance between X and Y is 0.040 m and between Y and Z is 0.060 m.

μ₀ = 4π × 10⁻⁷ T m A⁻¹.

A rectangular coil PQRS of one turn lies in the plane of the page between the poles of a magnet. The uniform magnetic field of flux density 0.050 T is directed from left to right, in the plane of the page. Sides PQ and RS are 0.060 m long and perpendicular to the field. Sides QR and SP are 0.040 m long and parallel to the field. The current in the coil is 2.5 A in the direction P → Q → R → S.

In an electron energy analyser, two large horizontal parallel plates are 10.0 mm apart in a vacuum. The potential difference between them is 150 V and the lower plate is positive. Electrons, each with a kinetic energy of 200 eV, enter the region between the plates through a small hole H in the lower plate, moving at 40° to the plate.

e = 1.60 × 10⁻¹⁹ C; m_e = 9.11 × 10⁻³¹ kg.

Close to the equator the Earth's magnetic field is horizontal and directed towards the north, with a flux density of 3.0 × 10⁻⁵ T. A cosmic-ray proton moves vertically downwards towards the surface at a speed of 2.0 × 10⁷ m s⁻¹. In the diagram, up the page is vertically upwards, the right of the page is north and east is out of the page.

e = 1.60 × 10⁻¹⁹ C; mass of a proton = 1.67 × 10⁻²⁷ kg.

An electron is accelerated from rest through a potential difference of 2500 V. It then enters, along the centre line, the region between two horizontal parallel plates that are 40 mm long and 20 mm apart. The potential difference between the plates is 240 V and the upper plate is positive. Ignore edge effects.

e = 1.60 × 10⁻¹⁹ C; m_e = 9.11 × 10⁻³¹ kg; g = 9.81 m s⁻².