Question

A positive electric charge Qis spread out uniformly along a wire of length Lplaced on the x-axis, with one end of the wire located at x=-L/2and the other at x=+L/2. Today we are going to find the electric field E=Exi+Eyjlocated at x=0,y=-adirectly below the midpoint of the wire. We will again use the idea of superposition: the total electric field at the point x=0,y=-a is due to the sum of the small electric fields produced by each piece of the charged wire.

1.

Take a little piece of the wire of length dxlocated at an arbitrary position xalongthe wire. What is the x-component of the field at the position x=0,y=-aproduced by this little piece of wire? Call it dEx.

2.For the same little piece of wire, what is the y-component of the field dEy?

3.Finally, sum up the pieces to get Eat the position in question. If you can argue that one or both components of Earezero without doing a full-blown integral, then by all means do so.

Answer 1