1 of 8 CTVoltageII 1 A minus charge q is brought in from infinity to be near a plus charge q The work done by the external agent is bringing the minus charge in from infinity is A positive B negative C zero from infinity q fixed q Answer Negative work was done by the external agent positive work was done by the field As the external agent tweezers brought the q charge toward the attractive q charge it had to restrain pull back on the q charge So force and displacement are in opposite directions and work done is negative CTVoltageII 2 The equipotential contours around two positive charges charges 1 and 2 are shown Which charge is larger A Charge 1 B Charge 2 A 1 40V 2 100V 100V 40V 15V 15V B A test charge q is carried from point A to point B The work done by the external agent carrying the test charge is A Positive B Negative C Zero Answers Charge 2 is the larger charge Near a point charge V equipotentials we have 100V kq Comparing the two 100V r kq i The charge with the large r must have the larger q A ri 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 2 of 8 better way to see this is to think of voltage as electrical height and regard the equipotential lines as contours lines of constant altitude V 100V x Answer for part 2 zero U q V Since V 0 then U 0 and the total work done is zero Positive work was done in the first half of the journey negative work was done in the second half the net work was zero 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 3 of 8 CTVoltageII 3 The equipotential surfaces around a line of charge into the page are shown Each equipotential is 2m from the nearest neighbor equipotentials What is the approximate magnitude of the electric field at point A A 0 1 V m B 0 2 V m 2 5V C 0 4 V m A 1 8V 2 3V D 0 6V m 2 1V E None of these 0V 1 4V G G The formula V E r can be used if r is a short enough distance so that E is G G approximately constant over that distance If r is parallel to E then G G V dV This formula says E V E r E r and we can solve for E E r dr is the rate of change of V volts per meter if you move along the direction of E We get the rate of change of V near point A by taking a relatively short r near A centered B on A is best and reading the V from the graph 2 5V For the l 2m chosen on the graph the voltage change is A 2 3V 1 8V l 2m V 1 8V 1 4V 0 4V 2 1V 0V 1 4V E V 0 4V 0 2V m r 2m The E field at point B is E 2 5V 2 3V 0 2V V 0 1V m r 0 2m 2m 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 4 of 8 CTVoltageII 4 Two test charges are brought separately into the vicinity of a charge Q First test charge q is brought a distance r from Q Then q is removed and a test charge 2q is brought a distance 2r from Q Which charge configuration required more work done by the external agent moving the test charge to assemble r A Q B q 2r Q 2q C Both required the same work Answer Both required the same work Work done is change in the potential energy U q V kQ For case I on left this is U q test V q For case II on right this is r kQ kQ U q test V 2q q 2r r 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 5 of 8 CTVoltageII 5 A constant uniform E field of magnitude E 1V m points up Point a is 2m 3m Point b is 5m 7m What is the voltage difference V b V a E 1 V m A 5 V b 5 7 B 4 V C 3 V 5m 4m D None of these 2 3 a 3m Answer None of these The voltage difference V b V a is 4V Point b is at a lower voltage than point A Remember E fields point from higher voltage to lower voltage G G V E r E y y 1 V m 4 m 4V 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 6 of 8 CTVoltageII 6 An electron in the vicinity of charges 1 and 2 is moved by an external agent at constant speed from position i to position f What is the work required to move the electron from i to f i f 1 40V 100V 2 100V 40V 15V 15V A 85 eV D 85 eV B More than 85 eV E None of these C Between 0 and 85eV Answer 85eV From the voltages on the equipotential lines you can see that the two charges are both positive The work done by an external agent in moving the electron is negative because in moving a negative electron closer to a positive charge the external agent actually has to restrain the electron hold it back Since the external force and the displacement are opposed the work is negative Wext PE q V e Vf Vi e 100V 15V e 85V 85eV 9 28 2009 PHYS1120 Dubson Fa09 University of Colorado 7 of 8 CTVoltageII 7 Two identical charges Q and Q are fixed in space The electric field at the point X midway between the charges is zero The voltage at that point is A Zero B Non zero E 0 V Q Q Answer The voltage is non zero At points near positive charges there is a positive voltage The only way to get zero voltage with point charges is to be infinitely distant from all charges or to have the negative voltages from negative charges exactly cancel the positive voltages from positive charges V Q 9 28 2009 PHYS1120 Dubson Fa09 V 0 here E slope 0 Q x University of Colorado 8 of 8 CTVoltageII 8 Two equal and opposite charges Q and Q are fixed in space The voltage at the point X midway between the charges is zero The electric field at that point is A Zero B Non zero E V 0 Q Q What sign work is done by an external agent to bring a negative charge q from infinity to point X A positive work B negative work C zero work Answers The E field is non zero The E fields from the two charges do not cancel there On a plot of voltage vs position the E field magnitude is proportional to the slope The work done by an external agent to bring any charge to that …
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