MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Exam One Solutions Problem 1(25 points):answers without work shown will not be given any credit. Four point-like objects of charge-20,+,-O,and +20 respectively are placed at the corners of a square of side a as shown in the figure below. +0 -0 a/2 a/2 +x + -2Q +2Q Part(a) Determine the electric field at the point P,which has coordinates()=(a/2,a) Express your answer in terms of k=1/4re,,a,i,and j as needed. Part(b) Choose infinity to be the zero point for the electric potential (V()=0).Determine the electric potential at the point P,which has coordinates (x)=(a/2,a).Express your answer in terms of k=1/4,a,i,and j as needed. Part(c) Determine the direction and magnitude of the electric dipole moment of this charge configuration.Express your answer in terms of k=1/4re,,a,i,and j as needed. 1
1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Exam One Solutions Problem 1 (25 points): answers without work shown will not be given any credit. Four point-like objects of charge −2Q , +Q , −Q , and +2Q respectively are placed at the corners of a square of side a as shown in the figure below. Part (a) Determine the electric field at the point P , which has coordinates (xP , yP ) = (a / 2,a). Express your answer in terms of k = 1/ 4πε 0 , Q, a , ˆ i , and ˆ j as needed. Part (b) Choose infinity to be the zero point for the electric potential (V (∞) = 0 ). Determine the electric potential at the point P , which has coordinates (xP , yP ) = (a / 2,a). Express your answer in terms of k = 1/ 4πε 0 , Q , a , ˆ i , and ˆ j as needed. Part (c) Determine the direction and magnitude of the electric dipole moment of this charge configuration. Express your answer in terms of k = 1/ 4πε 0 , Q , a , ˆ i , and ˆ j as needed
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