A point charge is fixed at the origin in free space

PHYSICS · Multi-part · CBSE · Physics · Electric Charges and Fields · Electric Charges and Fields

Problem

A point charge QQ is fixed at the origin in free space. Consider a general point R(x, y, z)R(x,\,y,\,z) on the Cartesian coordinate axes. Answer the following. Take k=9.0×109 N m2C−2k = 9.0\times10^{9}\,\text{N m}^2\text{C}^{-2}. (i) Derive expressions for the components ExE_x, EyE_y and EzE_z of the electric field at RR in terms of QQ, xx, yy, zz and the distance rr from the origin. (ii) Using the expressions obtained in part (i), find the electric-field vector at the point (0.03 m, 0.04 m, 0.12 m)(0.03\,\text{m},\,0.04\,\text{m},\,0.12\,\text{m}) when Q=+2.0 μCQ = +2.0\,\mu\text{C}. Give your answer in component form. (iii) Along the straight line joining the origin to the point specified in part (ii), at what distance from the origin will the magnitude of the electric field become one-tenth of the value calculated in part (ii)? Express your answer in centimetres.

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