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# WM2Solutions - SOLUTIONS WM2 Q21-21) Equal charges repel...

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SOLUTIONS – WM2 Q21-21) Equal charges repel each other, opposite charges attract. Thus, if the charges have opposite sign they will attract each other and the electric field lines will point from the positive charge to the negative charge; there is no zero electric field between them. For equal signs of the two charges the situation is different: The two charges repel each other, creating E = 0 somewhere on the line connecting the two charges. If charges Q sits at (0,0), then charge 2Q is at (l,0) (if we assume that the line connecting the two charges corresponds to the x-axis). Then the total electric field is given by the sum of the two contributions from each charge. Let us assume that both charges are positive. For a point somewhere between the two charges, the electric field from Q points to the right while the one from 2Q points to the left (electric field lines point from positive to negative charges). Thus, when we add the two contributions, we need to include a minus sign to take care of the different directions of E. The same is true if we chose two negative charges: Then the field from Q points to the left while the one from 2Q points to the right – again, we need the minus sign. Thus: = = 2 2 2 2 0 2 0 2 0 ) ( 2 ) ( 4 ) ( 4 2 4 l x x x l x Q l x Q x Q E πε . This is zero for l l l l l x l lx x l lx x x l x 41 . 0 ) 2 1 ( 2 0 2 0 2 ) ( 2 2 2 2 2 2 2 2 ± = + ± = + = + = Q22-1) The electric flux through a closed surface is defined as 0 ε encl E Q A d E = = Φ r r . If the flux is zero, the electric field does not necessarily have to be zero: Imagine a

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## This note was uploaded on 04/07/2008 for the course PHY 113 taught by Professor Jordan during the Spring '08 term at Rochester.

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WM2Solutions - SOLUTIONS WM2 Q21-21) Equal charges repel...

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