Physics 240 Fall 2003: Exam #1. Please print your name: Please list your discussion section number: Please list your discussion instructor:

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1 Physics 4 Fall 3: Exam #1 Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above. This will be a 1.5 hour, closed book exam. The exam includes questions. 3. You may use a calculator, please do not share calculators 4. You may use one 3 x5 note card with notes and equations you think may be useful. You can write on both sides of the card if you like. 5. You will be asked to show your University student ID card when you turn in your exam. ID checked by: Table of constants: ε = 8.85x1-1 C /Nm k = 1/(4πε ) q electron =-1.6x1-19 C q proton =1.6x1-19 C m electron =9.1x1-31 kg m proton =1.67x1-7 kg G = 6.67x1-11 Nm /kg

2 1: Imagine a uniform sphere of charge with a radius and total charge. A point charge q placed on the surface of this sphere feels a repulsive force F=kq/. I now remove a small sphere of charge, centered on a point / from the center of the sphere, with radius /, on the side opposite our test charge q. What is the magnitude of the force repelling q now? q Empty region q a) kq/ b) 17kq/18 c) 3kq/4 d) 7kq/8 e) kq/ : Three identical objects, each with charge, sit on corners of a square with edge length L. What is the magnitude of the electrostatic force on the charge in the upper right corner? a).8k /L b) k /L c) 1.4k /L d) 3.4k /L e).k /L L

3 3: Consider the electric dipole shown in the figure below. What is the electric field at a distance x along the perpendicular bisector of the dipole? k a) y ˆ x kd b) x ( d ) k c) ( x d ) y ˆ k d) xˆ d x 4 e) Zero 3 yˆ d - _ x ŷ xˆ 4: An infinite plane of charge creates an electric field which is uniform in space, and has a magnitude σ/ε. A finite disk of charge (radius ) creates a field which, along its central axis, has the value: σ z 1 ε z Now, imagine an infinite plane of charge with charge density σ, from which a hole of radius has been removed. What is the magnitude of the electric field at a point P a distance directly above the center of the hole? a) b) c) σ ε σ 4ε σ ( ) ε d) Zero σ e) 3ε P

4 5: An electron with charge q e and mass m e is fired with velocity v right down the center of two charged parallel plates. The charge density on the top plate is σ, and on the bottom plate it is -σ. If the width of the plates is W, what is the minimum velocity the electron must have to make it through the plates before hitting one side? σ a) b) qeσw m ε H e qeσh m ε W e v -σ W H c) qeσh m ε W e d) qeσw m ε H e e) meσw q ε H e 6: Which of the following statements is true concerning the electric field between two oppositely charged infinite parallel plates? a) It is zero midway between the plates b) It is a maximum midway between the plates c) It is at its maximum at the positively charged plate d) It is at its maximum at the negatively charged plate e) It is constant between the plates

5 7: A point charge rests inside a hollowed out region in an otherwise spherical conductor. A new point charge q is placed outside the conductor, a distance from its center. Which combination correctly describes the total force on q and the total force on? F on q F on a) Zero Zero b) kq / Zero c) Zero k / d) kq/ kq/ e) kq/ Zero q 8: Imagine a spherically symmetric distribution of charge with a charge density ρ that varies with radius. If I choose just the right variation of charge density with radius, this object will generate an electric field within it that is constant in magnitude. If I want to do this, what variation of charge density with radius must I choose? In this problem it may be useful to know that the charge enclosed in a sphere of radius is given by: a) ρ r b) ρ constant c) ρ 1/r d) ρ 1/r 3 e) ρ 1/r = 4πρ () r r dr

6 9: Consider two point charges, A and B, which have charges and 3 respectively. Both have mass M. The two charges are placed a distance apart and released so that they fly off in opposite directions. What is the final speed of point charge A when they are separated by a distance much greater than? a) 3 k M b) 3 k M c) k M 3k d) M e) k M Charge Mass M A Charge 3 Mass M B 1: Two conducting spheres separated by a distance many times their radii are charged so that the electric potential at their surfaces is the same. If the radii of the two spheres are 1cm and 3cm, and the total charge on the two spheres is 1x1-5 C, how much charge is on the smaller sphere? a) 5x1-6 C b) 1x1-5 C c) 1x1-6 C d).5x1-6 C e) 7.5x1-6 C 1cm 3cm

7 11: What is the magnitude of the Coulomb force exerted on a short uniformly charged rod (length L, total charge ) by a point charge q located a distance x from one end of the rod? kq a) ( x L ) kqx b) 3 L 3kq c) x kq d) x 1 L x 4kq e) 3 x L ( ) ( ) q x L 1: The electric field from an infinite line of charge with charge density λ (measured in C/m) is given by the equation: r λ E = rˆ πε r where r is distance from the center of the wire and rˆ is the unit vector pointing along the radial direction away from the wire. Consider a wire with charge density λ=5x1-8 C/m and a radius of 1 cm. An electron is released from rest at a distance 1 cm from the wire. What is the speed of the electron when it hits the surface of the wire? a) 7.x1 6 m/s b) 4.9x1 7 m/s c) 1.7x1 8 m/s d) 9.9x1 4 m/s e).7x1 7 m/s

8 Volts In the figure to the right there are three positive charges and one negative charge. The units on the x and y axis are meters. The lines show equipotential surfaces. They are spaced by 5V. The dotted line represents Volts, dashed lines are negative equipotentials, solid lines are positive. A few lines are labeled. In meters P S -5 Volts _ 5 Volts 1 Volts 13: What is the electric field at point P? a).35 V/m to the right b).35 V/m to the left c).6 V/m down d).6 V/m up e) Zero In meters 14: How much work must you do to move an electron from point to point S? a) 4.x1-18 J b) 9.x1-1 J c) -3.7x1-19 J d) -4.x1-18 J e) -9.x1-1 J

9 15: At the Fermi National Accelerator Laboratory in Illinois, protons are accelerated to very great velocity and smashed into anti-protons to study the interactions of particles. The proton acceleration process begins by ejecting protons from a metal cage which is held at a potential of 75, Volts above ground. What is the velocity of these protons when they are far from the cage? You may take the proton mass to be 1.67x1-7 kg and the proton charge to be 1.6x1-19 C. a) 4.5x1 6 m/s b) 1.7x1 9 m/s c) 1.x1 7 m/s d) 3x1 8 m/s e) 3.x1 4 m/s 16: Which of the following statements about electrostatic arrangements is not true? a) E is zero everywhere inside a conductor b) Equipotential surfaces are always perpendicular to E. c) No work is done by the electrostatic force when a charge moves along an equipotential line. d) If V is constant through a region of space, then E must be zero in that region. e) The electric force is zero on a charge when it rests on an equipotential line.

10 17: What is the equivalent capacitance of the set of capacitors shown in this figure? a) 4C b) C/ c) C d) C/4 e) C C C C C 18: A parallel plate capacitor with area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is the disconnected from the charging battery and its plate separation is decreased to d/, what happens to the potential difference between the plates? a) The potential difference is increased by a factor of four b) The potential difference is increased by a factor of two c) The potential difference is decreased by a factor of two d) The potential difference is decreased by a factor of four e) The potential difference remains unchanged

11 19: A spherical rubber balloon with radius r initial has total charge uniformly spread over its surface. Additional air is blown into the balloon, doubling its radius. How does the electric field at a point P which is 4r initial from the center of the balloon change as it expands? a) The electric field at point P doubles b) The electric field at point P is decreased by a factor of two c) The electric field at point P quadruples d) The electric field at point P is decreased by a factor of four e) The electric field at point P is unchanged : For the same expanding balloon how does the electric potential inside the sphere change as the sphere doubles in radius? Take the electric potential at infinity to be zero. a) The electric potential in the sphere doubles b) The electric potential in the sphere is decreased by a factor of two c) The electric potential in the sphere quadruples d) The electric potential in the sphere is decreased by a factor of four e) The electric potential in the sphere is zero before and after the expansion