Problems Week 8

# Problems Week 8 - Problems Week 8 8—1 8—3 The curves...

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Unformatted text preview: Problems: Week 8 8—1. 8—3. The curves show the paths (in xy—plane) of three particles in the presence of a constant 5 ﬁeld B = ~32 ' what can you say about the charge carried by each palticle? Why?‘ What is the force experienced by a conductor aligned along the z—axis if it carries a current of lOamps and is located in a g = —0.1Tz“ ﬁeld? Why? A cyclotron has an oscillator frequency of 12MHZ and a DEE radius of 53cm. What value of 5 would you need to accelerate deuterons (positive chargel .6 ><10"19 C). 8—4. 8—5. 8—6. In a constant L3 ﬁeld a charge with velocity Z J. E has a circular path of radius r = qB (i) If 13 || 2 what is the plane of the path. (ii) If you double V what happens to the angular velocity of the charge? Why? A proton travelling at 105 m/ s )2 is introduced between two parallel plates which have an E =100N/C 3”). What L3 ﬁeld would you apply so that the proton goes through un— deﬂected? [This is the principle of the velocity selector]. 10:. ii A S—turn coil of radius 50cm is lying ﬂat in the xz-plane. If it carries a current of lOamps ﬂowing counter clockwise, what is the magnetic moment (magnitude and direction). ' Y 8-7. 8-8. 8-9. If you apply a E ﬁeld of 0.1T, at an angle of 30° with respect to the y—axis, to the coil of problem 8-6, what is the torque (magnitude and direction) on the coil? The Biot—Savart law tells us that a current I ﬂowing through a conducting wire of length M , produces a 13 ~ﬁeld at Eu M) given by M .A_B. = ~”—°J * Z“: 47: r Show that the E ~ﬁeld lines circulate around the current. Since the 13 —ﬁeld due to a current swirls around it (like water circulates as it ﬂows out of a bath tub) Ampere taught us that the circulation of the 13 —ﬁeld around a closed loop 2 B - AZ C—._. is determined solely by the currents ﬂowing through the surface on which the loop is ' drawn. That is, EC§~A£ = #021,. —> where {no is a fundamental constant _ T~m ,uo =47r><10 7T Supposing we have a single current I ﬂowing along the y—axis. Please use ampere’s law and the symmetry of the problem to show that the. Q -ﬁeld at a point P in the xz— plane is given by #0] n B A :— _.(I) 27” where r is distance‘between P and the y~axis? 8—10. A tightly wound long solenoid consists of a large number of closely spaced rings with a '8211. common axis (see ﬁgure). It produces a uniform ﬁeld inside it. Use Ampere’s law to ShOW that for the case shown (cow current in Solenoid) ' ' Q : —,Lt0nb"c ‘ ' where a: No. of turns/meter of thesolenoid. (n=‘N/L) .M _ Ifr‘ l IKEl I r‘f/I wind 7 "‘ ' ’ "V In a mass spectrometer, the beam at 0 consists of two kinds of particles with same mass (M) but different charges (1;, q; entering with a velocity v = V)“; . For E = ~Bz” and the paths shown, what is the sign of the charge (+ive or ~ive)? Where will the larger charge land, P l or P2? Justify your answer. 8—12. Why do two parallel currents attract one another? 8—13. Shown is a coil of width b and length 16’ Suspended vertically in a 5 -ﬁeld. How would you make it work like a motor? The coil is free to rotate about its vertical axis. 8—14. A coil of cross-section {:1 : (2 x 3)m2ﬁ is being rotated about the vertical in the presence of a constant 5 : 0,2Tz . What is the maximum and minimum ﬂux of g through the coil? Why? 8-15. Imagine that a cube of side 1m is located at a height of mm above the Earth’s surface. I If. the ﬂux of E through 3 of the faces is 90yT — 1112 what must be the ﬂux through the other three? Why? 8—16. Write an essay on ~ “What is a Bar Magnet” I Starting from the idea that a single electron is a “bar magnet” of magnetic moment 9.27x10”24A ~m2. 8-17. Why does a bar magnet attract a piece of iron? ...
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Problems Week 8 - Problems Week 8 8—1 8—3 The curves...

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