Two point charges are held at rest in vacuum on the -axis: at and at

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential

Electricity, Magnetism and Electromagnetism, Ch Electrostatic potential, potential energy and the energy of the field

Problem

Two point charges are held at rest in vacuum on the xx-axis: q1=+4.0 nCq_1=+4.0\,\mathrm{nC} at x=0x=0 and q2=−1.0 nCq_2=-1.0\,\mathrm{nC} at x=0.30 mx=0.30\,\mathrm{m}. With V=0V=0 at infinity, the potential at a point on the axis between them isV(x)=14πε0[q1x+q20.30 m−x],0<x<0.30 m.V(x)=\frac{1}{4\pi\varepsilon_0}\left[\frac{q_1}{x}+\frac{q_2}{0.30\,\mathrm{m}-x}\right],\qquad 0<x<0.30\,\mathrm{m}. ((a)) Find the point between the charges at which V=0V=0. ((b)) At that point find Ex=−dV/dxE_x=-\mathrm{d}V/\mathrm{d}x, and state the direction of the field. ((c)) A student writes: “The potential there is zero, so a charge placed there feels no force.” Say in one or two sentences what is wrong with this.

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