PHY 131 Review Session Fall 2015 PART 1:


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1 PHY 131 Review Session Fall 2015 PART 1: 1. Consider the electric field from a point charge. As you move farther away from the point charge, the electric field decreases at a rate of 1/r 2 with r being the distance away from the charge. Now consider the electric field of a dipole. As you move farther away from the dipole, will the electric field decrease faster, slower, or the at the same rate as 1/r 2? Answer: The electric field falls off faster than 1/r Given the diagram of the two point charges, in what region will there be some location where the net electric field is zero? Answer: Region 1 3. The diagram shows a system of three point charges. If q 1 and q 2 are both 50cm from point x, and q 3 is 150cm from point x, calculate the electric field vector at point x.
2 Answer: E = x y V/m 4. Given the same electric field as question 2, calculate the force that a neutral charge experiences at point x, and the force a 6µC point charge would experience at point x. Answer: Neutral charge experiences 0 N, 6µC point charge experiences force F = x 23973y N. 5.
3 The half spherical shell has a radius b and a uniform surface charge density p s. At the center of the sphere (point O), in what direction will the electric field point? Answer: in the z direction pointing downward. 6. The ring of charge has a linear charge density λ = 2 C/m. The radius a = 4 m. Find the total electric field at point P, 15 m away from the center of the ring on the ring s central axis. Answer: E = 1.21*10 8 x V/m
4 7. a. What is the equivalent capacitance of the circuit? b. What is the charge on the 12µF capacitor? c. What is the voltage drop across the 12µF capacitor? d. What is the voltage drop across the 6µF capacitor? e. What is the charge on the 3µF capacitor? Answer: a) Equivalent Capacitance = 5.14µF b) Q = 51.4 µc c) V = 4.29 V d) V = V e) Q = 1.71 µc 8. a. Consider the circuit with an initially uncharged capacitor and two identical resistors. At the instant the switch is closed, what is the value of the currents I 1 and I 2? b. Assume the switch has been closed for a very long time, and is then reopened. Does the magnitude and/or direction of the current I 1 change?
5 c. Assume the switch has been closed for a very long time. What is the magnitude of current I 1? Answer: a) I 1 = ε/r I 2 = 0 b) Neither the magnitude or direction change c) I 1 = 0 PART 2: 1) Time Dependent Circuits: ( is the battery voltage (or other source of emf)) Time Constant Charging /Connected to source emf E Discharging/disconnected from emf 2) Given a distribution of (moving)charges and currents, find the magnetic field produced : a) Point charge moving with velocity v at point P (distance vector ) : Direction of field is perpendicular to the plane formed by velocity vector and distance vector (Use right hand thumb rule) Biot Savart Law
6 b) Very long straight wire at a distance r Direction of field is tangential to the circle of radius r c) Short straight segment Where the angles are the angles made by two ends at the point P and r is the perpendicular distance of the point from the segment. Direction of field is still tangential to the circle of radius r d) Center of single current loop of radius R and current I : Direction of field is perpendicular to the plane of circle e) At a distance X on the axis of single current loop of radius R and current I: Direction of field is perpendicular to the plane of circle f) Inside a long solenoid of N turns and length L If n turns/length is given then Direction of field is along the axis of solenoid 2. Magnetic field is present in the system and we have a moving charge or a current carrying conductor Magnetic Force on that element (Field produced by the charge or current is not considered while calculating magnetic force on that element) a) Charge q moving with velocity and magnetic field : Force is perpendicular to the plane formed by velocity vector and magnetic field vector b) Current I in an element of length dl:
7 If length l and magnetic field B do not change their direction c) Magnetic Torque on current loop: Magnetic moment Where is unit vector perpendicular to the plane of current loop Potential energy of a current loop: d) Induction Flux in a single loop: (If B is constant all along the area) Faraday s Law (for one loop): Self inductance Selfinduced emf Mutual inductance Induced emf means the flux in #2 due to #1 Magnetic energy: Stored in an inductor Energy Density in a B field
8 Current loop in a magnetic field. a) Net magnetic force on the current loop is equal to zero. b) There is a net torque on the current loop c) This torque will try to bring the axis of loop parallel to the direction of magnetic field so that the magnetic flux is maximum. d) If the current loop moves, an emf is induced in the loop which tries to increase current in the direction such that the magnetic field produced is opposite to the direction of given field Questions: 1) A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction. The beam travels a distance of cm while in the field. What is the magnitude of the magnetic field? 2) A long wire carrying 4.5A of current makes two 90 o bends. The bent part of the wire passes through a uniform 0.24 T magnetic field as directed as shown and confined to the limited space. Find the magnitude and direction of the force that the magnetic exerts on the wire. 3) Two parallel wires are 5 cm apart and carry currents in opposite directions. Find the magnitude and direction of the magnetic field at point P due to two 1.5 mm segments of wire that are opposite each other and each 8 cm form P.
9 4) A circular loop of wire is in a region of spatially uniform magnetic field. Determine the direction of the induced current in the loop a) B is increasing b) B is decreasing, c) B is constant. Explain your reasoning. 5) When the current in a toroidal solenoid is changing at a rate of A/s, the magnitude of the induce emf is 12.6mV. When the current equals 1.4 A, the average flux through each turn of the solenoid is Wb. How many turns does the solenoid have? 6) Switch S1 is closed while switch S2 is kept open. The inductance is L = H and the resistance is R = 120 Ohm. a) When the current has reached its final value, the energy stored in the inductor is 0.26 J. What is the emf E of the battery? b) After the current has reached its final value, S1 is opened and S2 is closed. How much time does it take for the energy stored in the inductor to decrease to 0.13 J, half the original value? Answer Key : 1) 0.67 * 10 ^(3) T 2) N, 63.4 degree below the direction of the current in the upper wire segment 4) A) Clockwise B) Counter clockwise C) Zero 5) 252 6) A) 255 V B) 0.67ms
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