227F24Exam1ATOPRINT

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School

Rutgers University**We aren't endorsed by this school

Course

PHYSICS 227

Subject

Electrical Engineering

Date

Dec 20, 2024

Pages

Uploaded by LieutenantDiscovery15472

Name___________ ID____________ PHY-227 Exam 1 (Version A) Before the Exam Starts1.You should have an exam questionnaire packet and an answer sheet in front of you. Do not open the exam questionnaire until instructed. 2.Make sure the answer sheet is pre-filled with your name and student ID. Write your name and ID at the top of this sheet. 3.On the answer sheet, fill in the bubble corresponding to the exam version at the top of this page. 4.No phone, calculator, smart watch, computer, tablet, or any other communication device allowed. Turn all devices off and put them away, close all bags. During the Exam 5.Do not speak to others while the exam is going on (even if you have finished). 6.Raise your hand if you have a question and the proctor will assist you. 7.Do not make marks on the answer sheet other than within the bubbles. After you have finished the Exam 8.Come up to the front of the room and hand in your answer sheet and exam packet. Do not speak to other students until after you hand in your exam and leave the room, otherwise we will assume you are sharing information.

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Analy&cal Physics 01:750:227 Equa%on sheet Charge, Coulomb’s Law, E-Fields - Module 1 ࠵?⃗!="#!#"$̂$"(Coulomb force) ࠵?%⃗="#$̂$"=#$̂&’(#$"(field from point charge) ࠵?⃗= ࠵?࠵?&⃗(force on charge) Electric Flux, Gauss’s Law - Module 2 Φ!= ∫ ࠵?&⃗∙ ࠵?࠵?⃗(electric ﬂux through surface) Φ!= ∮ ࠵?&⃗∙ ࠵?࠵?⃗#=$!"#%$(Gauss’s Law) ࠵? =&’()%$(field from infinite line of charge) ࠵? =*’%$(field from infinite plane of charge) Electric Poten%al - Module 3 ࠵?)="#!#"$(Electric Poten?al Energy 2 charges) ࠵? =+,%)(Electric poten?al single charge) ࠵? = − ∫ ࠵?&⃗∙ ࠵?࠵?⃗(Voltage from E field) ࠵?&⃗= −-.-)࠵?̂(field from poten?al) ࠵? = − ∫ ࠵?࠵?&⃗∙ ࠵?࠵?⃗(poten?al energy charge q in E field) ࠵? = ∑∑+,&,’)&’/01234/54214(poten?al energy of n charges) Capacitance -Module 4 ࠵? = ࠵?/࠵?(capacitance) ࠵? =6%$-(parallel plate capacitor) ࠵? =4’࠵?࠵? =4’࠵?࠵?’(stored energy) 47!(= ∑47&/214(capacitors in series) ࠵?8,= ∑࠵?2/214(capacitors in parallel) ࠵?9= ࠵?࠵?(capacitor with dielectric)

Constants Coulomb constant k = 8.99 x 109N-m2/C2Electric constant e0 = 8.85 x 10-12C2/N-m2 also (F/m) MagneBc constant μ0= 4px 10-7 T-m/A = 1.26 x 10-6T-m/A Avagadro’s number ࠵?6= 6.02 × 10’:Speed of light c = 3.00 x 108m/s Mass of electron 9.1 x 10-31kg Mass of proton 1.7 x 10-27 kg Charge of proton 1.60 x 10-19C Charge of electron -1.60 x 10-19C Geometrical Formulae Circumference of circle of radius R: 2࠵?࠵?Area of circle of radius R: ࠵? = ࠵?࠵?’Surface area of sphere of radius R: ࠵? = 4࠵?࠵?’Surface area of cylinder of radius R and length L: ࠵? = 2࠵?࠵?࠵?(side) + [2 × ࠵?࠵?’] (two ends) Volume of sphere of radius R: ࠵? =;:࠵?࠵?:Volume of cylinder of radius R and length L: ࠵? = ࠵?࠵?’࠵?Dot and Cross Product ࠵?⃗∙ ࠵?&⃗= |࠵?||࠵?| cos ࠵? = ࠵?<࠵?<+ ࠵?=࠵?=+ ࠵?>࠵?>࠵?̂ × ࠵?̂ = ࠵?M࠵?̂ × ࠵?M= ࠵?̂࠵?M× ࠵?̂ = ࠵?̂࠵?⃗× ࠵?&⃗= N࠵?=࠵?>− ࠵?>࠵?=O࠵?̂ − (࠵?<࠵?>− ࠵?>࠵?<)࠵?̂ + N࠵?<࠵?=− ࠵?=࠵?<O࠵?MCommon integrals ∫ ࠵?/࠵?࠵? =4/34࠵?/34∫4<࠵?࠵? = ln (࠵?)∫ sin ࠵? ࠵?࠵? = − cos ࠵?∫ cos ࠵? ࠵?࠵? = sin ࠵?V ࠵??<࠵?࠵? =1࠵?࠵??<

227 Fall 2024. Exam 1, version A 1.[Mod 1] Three charges are placed as shown, with a distance d between Q1and Q2and between Q2and Q3. If ࠵?!= +࠵?, ࠵?"= −࠵?, ࠵?#= +2࠵?,what is the magnitude and the direction of the force on Q3due to the other two charges? (note: k =Coulomb constant) ©Rutgers University 2024a.0 b.#$%!"&!to the right c.#$%!"&!to the left d.’$%!"&!to the right e.’$%!"&!to the left 2.[Mod 1] Two charges are placed as shown. If ࠵?!= +3 ࠵?, ࠵?"= −5࠵?, ࠵?!= 1 ࠵?, ࠵?"= 2 ࠵?, what is the magnitude of the electric field at the origin? (note: k =Coulomb constant) ©Rutgers University 2024a.࠵?)3"+ +’(,"b.k 4.25 c.࠵?)3"+ +’","d.k 2.75e.࠵?)−(3") + +’(,"

3.[Mod 2] The figure shows 5 Gaussian surfaces, enclosing various combinations of 4 charges. Which surface(s) has (have) the most positive total ﬂux through it. ©Rutgers University 2024a.S2and S5tied, all others less b.S2, S4, and S5 tied, all others less c.S1d.S1and S3tied, all others less e.S34.[Mod 2] A solid non-conductingsphere with radius 0.5 m and a uniform charge distribution is surrounded by a thick conductingshell, with an inner radius of 2 m and outer radius of 2.5 m. If the total charge on the inner sphere is 2 C and the total charge on the outer sphere is -4 C, what is the magnitude and direction of the electric field at a distance 3 m from the common center of the spheres? ©Rutgers University 2024a.2k/9 pointing outward b.2k/9 pointing inward c.4k/9 pointing inward d.4k/9 pointing outward e.2k/3 pointing inward

5.[Mod 3] Consider three charges, ࠵?!= −࠵?, ࠵?"= +2࠵?, ࠵?#= −࠵?. If their potential energy is taken to be zero when they are infinitely far apart, what is their potential energy when arranged as shown? ©Rutgers University 2024a.)$%!"&b.*)$%!"&c.!’$%!!+&!d.*!’$%!!+&!e.0 6.[Mod 3] A solid conducting sphere with radius a=1 m, is concentric with and surrounded by a conducting spherical shell with inner radius b=2 m, and outer radius c = 3 m. The inner sphere has a charge of +4 C on it, while the outer spherical shell has net negative charge of -4 C, on it. If the electric potential is taken to be zero at ࠵? = ∞, what is the potential at the center of the inner sphere? ©Rutgers University 2024a.0 b.4kc.kd.1.6 ke.2k

7.[Mod 4] Three capacitors are connected as shown with C1= C, C2= 2C, C3= 3C. Initially S1is closed and S2is open, as shown on the left, until C1and C2are fully charged. Then S1is opened first, and S2is closed next, as shown on the right. What is the voltage across C2after a long time? ©Rutgers University 2024a.1/6 V b.1/2 V c.1/3 V d.V e.2 V 8.[Mod 4] A parallel-plate capacitor has an initial plate separation of d. The capacitor is connected to battery and fully charged with initial potential di]erence V, and an initial stored energy U. The battery is disconnected from the capacitor, thenthe plate separation is increased to 2d and a dielectric with k= 2.0 is placed between the plates and fully fills the gap. What will the final stored energy be? ©Rutgers University 2024a.U/4 b.U/2 c.U d.2U e.4U

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