Physics 2: Physical Science & Technology (PHYC10004)
Week 6
Discussion Questions
1
A hydrogen atom that has lost its electron is moving east in the region where the magnetic field is directed from south to north. It will be deflected:
a) up b) down c) north d) south e) not at all.
2
Which of the following statements is correct:
When a charge moves in a uniform magnetic field (but not parallel to the magnetic field):
a) the magnitude of its velocity and momentum changes
b) the direction of its velocity and momentum changes
c) its kinetic energy changes
d) its acceleration changes.
3
In the figure, the current element idl , the point P, and the three vectors (1, 2, 3) are all in the plane of page. The direction of the infinitesimal magnetic field dB generated by this current element at the point P is:
(a) in the direction marked “1”
(b) in the direction marked “2”
(c) in the direction marked “3”
(d) out of the page
(e) into the page.
4
Four long straight wires carry equal currents into the page as shown. The magnetic force exerted on the wire F is:
(a) north (b) east (c) south (d) west (e) zero.
Problem Solving Questions
5
An electron (mass m = 9.1 ×10–31 kg, charge e = –1.6 ×10–19 C) is projected with a velocity of 1.3 ×107 m s–1 at an angle of 30。to a uniform magnetic field of strength B = 0.2 T.
(a) Find the component of the velocity along the magnetic field initially.
(b) Find the component of the velocity perpendicular to the magnetic field initially.
(c) Describe the trajectory of the electron.
(d) Find the radius of the resulting electron trajectory in the plane perpendicular to the magnetic field.
(e) Find the period of the motion.
(f) How far does the electron move along the field direction during one full revolution?
6
A mass spectrometer, sketched schematically below, has a source that produces singly charged ions. The ions are oxygen 16u (u is an atomic mass unit), carbon 12u, and an unknown element. The ions travel through perpendicular electric and magnetic fields, exit from a narrow slit S, and move in semicircular paths in a region of uniform magnetic field, as shown. Each species of ion makes a line on the photographic plate at the point where it strikes the plate. The carbon and oxygen lines are separated by 2.25 cm. The unknown element makes a line between them 1.16 cm from the carbon line.
(a) Show that all ions entering the narrow slit S must have the same velocity. Hint: consider the relationship required between E and B.
(b) Which element gives rise to the line on the photographic plate furthest from the slit?
(c) Calculate the mass of the unknown element (in units of u).
7 (The Hall Effect)
A current runs from left to right in the rectangular conductor shown to the right below.
The conductor is immersed in a magnetic field directed into the page.
Point S is measured to be at a higher potential than point T.
(a) In what direction do charge carriers move inside the conductor if
• they are positively charged, and
• if they are negatively charged?
(b) What are the polarities of the upper and lower sides of the conductor?
(c) From (a), (b), and the direction of the magnetic field, deduce the sign of the charge carriers in the conductor.
8
A physicist is designing a cyclotron to accelerate protons to one-tenth the speed of light. The magnet used will produce a field of magnitude of 1.4 T. Ignoring relativistic effects, calculate
(a) the required radius of the cyclotron ‘Dees’, and
(b) the corresponding oscillator frequency.
9
Two long straight wires are parallel and carry current in the same direction. The currents are 8.0 and 12.0 A and the wires are separated by 0.40 cm.
(a) Indicate the direction of the magnetic field at a point midway between the wires.
(b) Calculate its magnitude at the point midway between the wires.
(c) At what point between the wires is the magnetic field zero?
10
Using the Biot-Savart law show that the magnetic field at point P at the centre of the semicircle shown, is given by B = µ0I/4R.
11
The windings of a very long coil (a solenoid) are made of a wire 0.8 mm in diameter. The turns j u st touch each other (but are made of insulated wire). Find the magnetic field inside it if it carries a current of 2 A.
12
Two thin, hollow, cylindrical, coaxial conductors with radii a and b (b>a) carry currents I which are equal in magnitude and oppositely directed. Ignoring the thickness of the conductors, demonstrate that the magnetic field in the volume:
(a) r < a, contained by the inner cylinder, is zero;
(b) a < r < b, between the conductors, is B = µ0I / 2πr;
(c) r > b, outside the outer cylinder, is zero.
13 ( mini-challenge question )
The figure below shows a cross section of an infinite conducting sheet carrying a current per unit x-length of λ; where the current emerges perpendicularly out of page.
(a) Use the Biot-Savart law and symmetry to show that for all points P above the sheet, and all points P′ below it, the magnetic field B is parallel to the sheet and directed as shown.
(b) Use Ampere’s law to prove that B = 0.5µ0 λ at all points P and P′ .
Past Exam Questions
14
An alpha particle (q = +2e, m = 6.65 × 10一27kg) travels in a circular path of radius 4.50 cm in a uniform. magnetic field with B = 1.20 T.
(i) Calculate its speed.
(ii) Calculate the frequency of revolution of the alpha particle.
15
Consider two very long parallel wires that are placed equal distances from they-axis and carry equal currents directed into the page, as shown in the figure below left.
(a) What is the direction of the magnetic field at point P on they-axis?
(b) If a long wire carrying a current into the page is now placed at point P (shown in the right figure) what will be the direction of the magnetic force on the wire? Explain your reasoning.
16
A circular loop of wire radius R carries a steady current i as shown in the diagram.
(i) Determine the magnitude of the magnetic field Bz at the point located a distance z m above the centre of the loop and along the axis of the loop. What is the direction of the z-component of if the direction of i is as shown in the diagram?
(ii) Show that if Z ≫ R, the expression from part (i) simplifies to