InterviewSolution
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InterviewSolution
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Two points charges are located on the x-axis, `q_1=-1muC` at `x=0 and q_2=+1muc` at `x=1m`. a. Find the work that must be done by an external force to bring a third point charge `q_3=+1muC` from infinity to `x=2m`. b. Find the total potential energy of the system of three charges. |
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Answer» Correct Answer - A::B::C::D a. The work that must be done on `q_3` by an external force is equal to the difference of of potential energy `U` when the charge is at `x=2m` and the potential energy when it is at infinity. `:. W=U_f-U_i` `=1/(4piepsilon_0) [(q_3q_2)/((r_32)_f)+(q_3q_1)/((r_31)_f)+(q_2q_1)/((r_21)_f)]-1/(4piepsilon_0)[(q_3q_2)/((r_31)_i)+(q_3q_1)/((r_31)_i)+(q_2q_1)/((r_21)_i)]` Here `(r_21)_i=(r_21)_f` and `(r_32)_i=(r_31)_i=oo` `:. W=1/(4piepsilon_0)[(q_3q_2)/((r_32)_f-(q_3q_1)/((r_31)_f)]` Substituting the values, we have `W=(9.0xx10^9)(10^-12)[((1)(1))/((1.0))+((1)(-1))/((2.0))]` `=4.5xx10^-3J` b. The total potential energy of the three charges in given by `U=1/(4piepsilon_0)((q_3q_2)/r_32+(q_3q_1)/r_31+(q_2q_1)/r_21)` `=(9.0xx10^9)[((1)(1))/((1.0))+((1)(-1))/(2.0))+((1)(-1))/((1.0))](10^-12)` `=-4.5xx10^-3J` |
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