The electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in an equation
Find an expression for the electric field when the rod is infinitely long.
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When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Let's see what happens if we break a finite rod up into a small number of finite particles. The figure shows a rod of length 2l carrying a uniform charge Q modelled as two particles of charge Q/2. The particles are at the ends of the rod.
Find an expression for the electric field at point A located at a distance l above the midpoint of the rod by using the exact expression:
When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Let's see what happens if we break a finite rod up into a small number of finite particles. The figure shows a rod of length 2l carrying a uniform charge Q modelled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located at a distance l above the midpoint of the rod by using the exact expression
A thin rod of length l and uniform charge per length lies along the x-axis as shown in Figure P23.8 (a) Show that the electric field at P, a distance d from the rod along its perpendicular bisector, has no x component and is given by . (b) What if? Using your result to part (a), show that the field of a rod of infinite length is .
