This set of lecture-oriented practice questions was developed under a Round One ALG Textbook Transformation Grant

Saha, Arun

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GALILEO, University System of Georgia

GALILEO, University System of GeorgiaGALILEO Open Learning MaterialsPhysics and Astronomy Ancillary Materials Physics and AstronomySpring 2015Magnetic Fields, Voltage, and Currents Problems(Practice Questions)Arun SahaAlbany State University, arun.saha@asurams.eduFollow this and additional works at: http://oer.galileo.usg.edu/physics-ancillaryPart of the Physics CommonsThis Homework is brought to you for free and open access by the Physics and Astronomy at GALILEO Open Learning Materials. It has been acceptedfor inclusion in Physics and Astronomy Ancillary Materials by an authorized administrator of GALILEO Open Learning Materials. For moreinformation, please contact affordablelearninggeorgia@usg.edu.Recommended CitationSaha, Arun, "Magnetic Fields, Voltage, and Currents Problems (Practice Questions)" (2015). Physics and Astronomy AncillaryMaterials. Paper 1.http://oer.galileo.usg.edu/physics-ancillary/1Magnetism Force on a Moving Charge in Magnetic Field Basic principle for voltage generation in a conductor or a  close loop conductor                                                                                                                          v B=2 Tesla F q In the magnetic field shown in the picture, what is the magnitude & direction of force on the charge 3 C moving at velocity of 100 m/s in the north direction. Magnitude of force F=q(vXB)                                    = 3*(100*2)=600 N From the right hand screw rule, the direction of the force F is in the RIGHT or in the EAST In the figure 1, a point charge +q C is moving at a velocity of V m/s towards NORTH. Magnetic field (B) direction is shown. What is the direction of the force on the charge: (a) East (b) West, (c) North, (d) South In the figure 1, a point charge +q C is moving at a velocity of V m/s towards SOUTH. Magnetic field (B) direction is shown. What is the direction of the force on the charge: (a) East (b) West, (c) North, (d) South Figure 1 In the figure 1, a point charge +q C is moving at a velocity of V m/s towards EAST. Magnetic field (B) direction is shown. What is the direction of the force on the charge: (a) East (b) West, (c) North, (d) South In the figure 1, a point charge +q C is moving at a velocity of V m/s towards WEST. Magnetic field (B) direction is shown. What is the direction of the force on the charge: (a) East (b) West, (c) North, (d) South Force on a moving charge in magnetic field Ampere’s Law What is the magnetic field at 5 cm far from a long straight conductor which carries 10 A current. Solution: B=I/(2pr) = 31.84 A/m I B B Current I Magnetic field from a long and straight wire Force on a Current Carrying Conductor in Magnetic Field In the magnetic field shown in the picture, what is the magnitude & direction of force on the 3 m conductor carrying current I=2 A  Magnitude of force F=I(LXB)                                    = 2*(3*2)=12 N From the right hand screw rule, the direction of the force F is in the LEFT or in the WEST X                              X                              X                              X                              I B=2 Tesla F 1. Conductor AB is falling down in Fig 1. What is the voltage VAB Answer: zero voltage [ Think why] B A B A 2. Conductor AB (=2m) is falling down in the magnetic field (0.1 mT) as indicated in the Fig.2. What is VAB when its velocity is 20m/s? What is the direction of current? Answer: 4 mV & current direction is from A to B  3. A small bicycle generator has 150 turns of wire in a circular coil of radius 1.8 cm. The magnetic field is 0.2 T. If induced voltage amplitude is 4.2 V, what is the rotational speed in r.p.m ? [1300 rpm]  Several variables here, so several problems from here.  Fig. 1 Fig. 2 Voltage & Current in a Conductor Moving in Magnetic Field Voltage & Current in a Conductor Moving in Magnetic Field v I Motion of electron I I I Try to understand the current direction in the moving conductor from the following equation: B for one free valance electron in conductor. 𝐹 = −1.6 × 10−19 𝑣 × 𝐵  In the test, direction of B or v will be given and you have to find the current direction in the closed loop circuit. Voltage & Current in a Conductor Moving in Magnetic Field In the test, direction of B or v will be given and you have to find the current direction in the closed loop circuit. v I Motion of electron I I I 𝐸 = 𝑙 𝑣 × 𝐵  = Blv l Current direction can be also found from this equation by applying right hand screw rule. Problem: In the magnetic field shown in the picture, what is the magnitude of voltage and & direction of current in 4 m conductor which is moving in east direction at a velocity of 10m/s. Here l is conductor length Solution: Magnitude of voltage E = Blv= 2Tesla*4m*10m/s=80Volts Direction of current is in NORTH direction B=2 Tesla Voltage in a Closed Loop Conductor in Magnetic Field ~ Faraday’s Law ~ 𝐸 = −𝑁ΔɸΔ𝑡 Here N=# of turns Δɸ=Magnetic flux change in the loop B=Magnetic field change in Tesla Δ𝑡=Change in time  = −𝑁BAΔ𝑡 Problem: A 40 turn coil of wire of radius 3 cm is placed between the poles of an electromagnet. The field increases from 0.75 Tesla to 1.5 Tesla at a constant rate in a time interval of 225 s. What is the magnitude of induced voltage in the coil if the field is perpendicular to the plane of coil. Solution:  E = -NBA/ Δ𝑡                     =-40*(1.5-0.75)*3.14*(0.03)^2/225                     =-0.38mV Magnitude of the induced voltage is 0.38 mV Voltage Generation in Power Industry 𝐸 = 𝜔𝑁𝐵𝐴𝑠𝑖𝑛 𝜔𝑡  E= Voltage generated ω=Rotational speed N=# turns B=Magnetic field A= Area of loop In power industry, voltage is generated by rotating  coils in fixed magnetic field as shown in the picture.  N S Problem: A small bicycle generator has 150 turns of wire in a circular coil of radius 1.8 cm. The magnetic field is 0.2 T. If induced voltage amplitude is 4.2 V, what is the rotational speed in r.p.m ? [137.5 rpm]     This problem is done in class. So see the note.  Several variables here, so several problems from here could be.   R-L-C Circuit Solution In the following R-L-C circuit, R= 2 Ohms, L=0.02 H  C= 0.001 F, and supply voltage is v=100sin(200t). Determine (a) total impedance of the circuit, (b) I_rms, (c) power loss in the resistor, (d) resonance frequency of the circuit, (e) power factor of the circuit, (f) whether current leading or lagging voltage Answer: (a) Z=2.2361 Ohms, (b) I_rms=31.6223 A, (c) 1999.939 Watts, (d) 35.606 Hz, (e) 0.8944, (f) Current leads Voltage 

Magnetic Fields, Voltage, and Currents Problems (Practice Questions)

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Magnetic Fields, Voltage, and Currents Problems (Practice Questions)

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