Magnets and Electromagnetism
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1 Review 9 Magnets and Electromagnetism 1. A 1.2 cm wire carrying a current of 0.8 A is perpendicular to a 2.4 T magnetic field. What is the magnitude of the force on the wire? 2. A 24 cm length of wire carries a current and is perpendicular to a 0.75 T magnetic field. If the force on the wire is 1.8 N, what is the current in the wire? 3. A 0.5 cm length of wire carries a 26 A current to your right in a 0.75 T magnetic field directed up. a. What is the direction of the force on the wire? b. What is the magnitude of the force on the wire? 4. A 4.5 m length of wire carries a 2.1 A current and is perpendicular to a magnetic field. If the wire experiences a force of 3.8 N from the magnetic field, what is the magnitude of the 5. A length of wire carrying a current of 2 A is perpendicular to a 6.5 T magnetic field. What is the length of the wire if it experiences a force of 2.99 N? 6. An electron beam is perpendicular to a 0.02 T magnetic field. What is the force experienced by one electron if the beam has a velocity of m/s? 7. A moving proton experiences a force of N when it travels at a right angle to a 1.35 T magnetic field. What is the velocity of the proton? 8. A doubly ionized particle travels upward with a speed of m/s through a magnetic field with a strength of 1.5 T to the east. What is the force experienced by the particle? 9. An electron traveling m/s at a right angle to a magnetic field experiences a force of N. What is the strength of the 10. A positively charged particle travels at a right angle through a 3 T magnetic field with a velocity of m/s. If the par- ticle experiences a force of N as it travels through the magnetic field, what is the charge on the particle? 11. A screen of ten straight wires is laid horizontally in an upward magnetic field of 24 T. Each wire carries a current of 12 ma and is 50 cm long. a. What is the total force experienced by this screen? b. If the force acts to the east what is the direction of the current? 12. A 15-cm length of wire is suspended horizontally in a magnetic field of 8 T oriented at a right angle to the wire in such a way that the force experienced by this wire acts in the upward direction. a. If the wire has a mass of 3 g and is able to move freely, what current running through this wire is necessary to lift the wire off the ground? b. If this wire is turned 90 so that the direction of the current lines up with the magnetic field, what happens to the force? 13. A square loop of current carrying wire is placed horizontally in a magnetic field that also is oriented horizontally. Sketch the layout and describe the forces on each segment of wire and the resulting force or motion if the wire is able to move freely. 14. An electron passes through a northward magnetic field of 0.40 T. It is determined that the electron experiences an upward force of N. a. What is the velocity (magnitude and direction) of the electron? b. What force would a neutron experience under these same conditions? 1
2 15. The speed of charged subatomic particles may be calculated by measuring their curved orbits due to centripetal forces when passing through a strong magnetic field. If a proton circles in an orbit of 3.1 cm within a magnetic field of 8 T, how fast is this proton moving? 16. How strong and in what direction would a magnetic field have to be to offset the force of gravity acting on an electron traveling at a speed of m/s to the north? 17. A 21 cm length of wire moves perpendicular to a 2.45 T magnetic field at 3.5 m/s. a. What is the magnitude of the EMF induced in the wire? b. The wire is part of a circuit with a total resistance of 3 Ω. What is the current through the wire? 18. An induced EMF of V is induced in a 5 cm wire when it is moved perpendicular to a magnetic field at 2.1 m/s. What is the magnitude of the 19. An unknown length of wire moves perpendicular to a 3.4 T magnetic field with a velocity of 12 m/s. If the induced EMF is 49 V, what is the length of the wire? 20. A straight wire that is oriented east-west is 28 cm long moves northward through a downward magnetic field of 2 T at a constant speed of 3.25 m/s. If the wire is 0.3 Ω, what is the magnitude and direction of the induced current in the wire? 21. Electrons moving at a speed of m/s travel undeflected through crossed electric and magnetic fields. If the strength of the electric field is N/C, what is the strength of the magnetic field? 22. A wire carries a current of 6 A. The wire is at right angles to a uniform magnetic field, and 0.8 m of the wire is in the field. The force on the wire is 0.62 N. What is the strength of the 23. A wire is at right angles to a uniform magnetic field with magnetic induction of 0.4 T. The current through the wire is 4 A. What is the force that acts on the wire when 60 cm is in the field? 24. A wire carries a current of 12 A. The wire is at right angles to a uniform magnetic field that exerts a force of 0.5 N on the wire when 2 m of the wire is in the field. What is the strength of the magnetic field? 25. A wire is at right angles to a magnetic field that exerts a force of 2.4 N on the wire. A current of 8.6 A flows through the wire. The induction of the magnetic field is 0.66 T. What length of wire is in the field? 26. A high-speed electron travels at right angles to a magnetic field that has an induction of 0.42 T. The electron is traveling at m/s. What is the force acting on the electron? 27. A straight wire that is 0.42 m long has a constant speed of 12 m/s perpendicular to a magnetic field that has a strength of T. a. What is the induced EMF in the wire? b. If the wire is part of a circuit that has a resistance of 2.25 Ω, what is the current through the wire? 28. A 25.5 m wire moves perpendicular to a magnetic field of T at a speed of 14.4 m/s. What EMF is induced in the wire? 29. The current carried through a wire is 13.4 ma. The wire is connected across a circuit with 5.5 Ω of resistance. If 1.12 m of the wire is moving perpendicularly through a magnetic field of 0.25 T, then what is the velocity of the wire? 30. A proton moving at a speed of m/s enters a magnetic field with a strength of 1.2 T and moves in a circle. What is the radius of the proton s path? 2
3 1 F = ILB ( 0.012$m) ( 2.4$T) F = 0.8$A F = 0.023$N 2 F = ILB 3a 3b I = F LB 1.8$N I = ( 0.24$m) 0.75$T I = 10$A The force is directed toward you. F = ILB ( 0.005#m) ( 0.75#T) F = 26#A F = 0.098#N 4 F = ILB 8 F = qvb 9 F = qvb ( 4.1" "10 4 "m/s)( 1.5"T) F = 2" "1.602" "10 19 "C F = 2.0" "10 14 "N The direction of the force is north. F qv 10 F = qvb 2.9$ $10 11 $N ( 1.602$ $10 19 $C) 8.6$ $10 7 $m/s 2.1$T q = F vb 4.32% %10 13 %N q = ( 4.5% %10 5 %m/s) 3%T q = 3.2% %10 19 %C%=%2e 5 F = ILB 6 F = qvb F LI 3.8$N ( 4.5$m) 2.1$A 0.40$T F IB 2.99$N ( 2$A) 6.5$T 0.23$m 7 F = qvb ( 9.8& &10 3 &m/s)( 0.02&T) F = 1.602& &10 19 &C F = 3.1& &10 17 &N v = F 6.9$ $10 13 $N v = ( 1.602$ $10 19 $C) 1.35$T v = 3.1$ $10 6 $m/s 11a 11b 12a 12b 13 F = ILB ( 0.5%m) ( 24%T) F = 0.012%A F = 0.144%N The net force will be 1.44 N The direction of the force is to the north. F g mg = ILB I = mg LB ( 9.8$m/s ) 2 ( 8$T) I = 0.003$kg 0.15$m I = 0.024$A The force will become zero. 3
4 14a 14b F = qvb v = F 9" "10 12 "N v = ( 1.602" "10 19 "C) 0.40"T v = 1.4" "10 8 "m/s The force is directed to the west. A neutron would experience no force. 15 F c mv 2 = qvb r v = r m ( 8&T) ( 0.031&m) v = 1.602& &10 19 &C 1.67& &10 27 &kg v = 2.4& &10 7 &m/s 16 F g mg = qvb 17a 17b mg qv ( 9.11$ $10 31 $kg) 9.8$m/s $ $10 19 $C ( 9.5$ $10 7 $m/s) 5.9$ $10 19 $T The field needs to point to the east. EMF = BLv ( 0.21%m) ( 3.5%m/s) EMF = 2.45%T EMF = 1.8%V I = 1.8$V 3$Ω I = 0.6$A 18 EMF = BLv EMF Lv 0.089%V ( 0.05%m) 2.1%m/s 0.85%T 19 EMF = BLv 20 EMF Bv 49#V ( 3.4#T) 12#m/s 1.2#m I = BLv R ( I = 2"T )( 0.28"m) ( 3.25"m/s) I = 6.1"A 0.3"Ω The current flows to the west. 21 F E Eq = qvb E v 22 F = ILB 23 F = ILB 4.2$ $103 $N/C 1.8$ $10 6 $m/s $T F LI 0.62%N ( 0.8%m) 6%A 0.13%T F = 4"A ( 0.6"m) ( 0.4"T) F = 0.96"N 4
5 24 F = ILB 25 F = ILB 26 F = qvb 27a F LI 0.5$N ( 2$m) 12$A 0.021$T F IB 2.4$N ( 8.6$A) 0.66$T 0.42$m ( 3.46& &10 7 &m/s)( 0.42&T) F = 1.602& &10 19 &C F = 2.3& &10 12 &N EMF = BLv ( 0.42$m) ( 12$m/s) EMF = 0.05$T EMF = 0.25$V 29 I = BLv R v = IR BL ( 5.5&Ω) ( 1.12&m) v = &A 0.25&T v = 0.26&m/s 30 F c mv 2 = qvb r r = mv ( 2& &10 5 &m/s) ( 1.2&T) r = 1.67& &10 27 &kg 1.602& &10 19 &C r = &m 27b I = 0.25%V 2.25%Ω I = 0.11%A 28 EMF = BLv ( 25.5$m) ( 14.4$m/s) EMF = 4.42$ $10 4 $T EMF = 0.16$V 5
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