For each of the following charge configurations, discuss which would be the best

Question

For each of the following charge configurations, discuss which would be the best approach for finding the electric field along the z-axis (you do not need to derive equations or solve for the field). Ensure you include mention of each of the three approaches in your answers to each configuration.

(a) Four equal charges placed at the corners of a square of side length L sitting in the x-y plane (centred at the origin)

(b) A wire of length L with a net positive charge (uniformly distributed). The wire lies along the x-axis with the mid-point of the wire being at the origin

(c) An infinite plane of charge in the x-y plane Part B (Advanced) For one of the above charge configurations, develop general expressions (summation or integral) for the electric field or potential along the z-axis for each of the three approaches. (You do not need to solve your expressions). Where it is not possible to develop an expression, then you should explain why this can’t be done.

Explanation / Answer

a)

we can simply calculate the electric field by each charge at the corners of the square and the do the vector addition.

b)

we first calculate the charge per unit length. we then consider a small length at some distance from center and derive the expression for charge on this small element. we calculate the electric field by this small element of the wire and then perform the integration to calculate the total electric field by the whole wire

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