A line charge, 2-Coulomb per meter, extended from (0,5m) to (10m, 5m). Superman

Question

A line charge, 2-Coulomb per meter, extended from (0,5m) to (10m, 5m). Superman plucked the line charge at the middle such that the line charge was still anchored at (0,5m) but the midpoint was 2.5-m higher than before. Compute the numerical electric field vector at (0, 0). When having difficulty in the evaluation of the one variable definite integral, use 5 values to represent the integrand and compute the area. Hint: think about a triangle with line charge and observer distance as its sides in geometry.

Explanation / Answer

Consider a system of two point-like objects with charges, q1 and q2 , separated by a distance r in vacuum. The electric force exerted by q1 on q2 is given by Coulomb's law, ! F12 = ke q1 q2 r 2 rˆ , (2.2.1) where ke is the Coulomb constant, and rˆ = ! r / r is a unit vector directed from q1 to q2 as illustrated in Figure 2.2.1(a). Similarly, the force on q1 due to q2 is given by ! F12 = ! ! F21 , as illustrated in Figure 2.2.1(b). This is consistent with Newton's third law.

Note that electric force is a vector that has both magnitude and direction. In SI units, the Coulomb constant ke is given by 9 2 2 0 1 8.9875 10 N m /C 4 e k !" = = # $ ,

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