Three collinear point charges are fixed on the -axis in air: at

PHYSICS · Subjective · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Three collinear point charges are fixed on the xx-axis in air: +3 μC+3\,\mu\text{C} at x=−0.10 mx=-0.10\,\text{m}, −5 μC-5\,\mu\text{C} at x=0x=0, and +2 μC+2\,\mu\text{C} at x=0.20 mx=0.20\,\text{m}. (i) Write the expression for the total electric potential V(x)V(x) at a general point P(x,0)P(x,0) on the xx-axis produced by the three charges. (ii) Show that setting V(x)=0V(x)=0 leads to different quadratic equations for the regions (a) x<−0.10 mx<-0.10\,\text{m}, (b) −0.10 m<x<0-0.10\,\text{m}<x<0, (c) 0<x<0.20 m0<x<0.20\,\text{m}, and (d) x>0.20 mx>0.20\,\text{m}. (iii) Solve the appropriate equation(s) to obtain all real positions on the xx-axis where the potential is zero. Specify clearly the region to which each solution belongs. (iv) State whether any of the zero-potential points lie between two of the charges and justify your conclusion. (Take 14πε0=9×109 N m2C−2\dfrac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}.)

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