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Question: In Fig. 24-54, how much work must we do to bring a particle, of chargeQ=+16eand initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of chargesq1=+4Eandq2=-q1/2? Distance,d=1.40cm,θ1=43°andθ2=60°

Short Answer

Expert verified

Answer:

The work that must be done to bring the particle is 0J.

Step by step solution

01

The given data

The given values of charges and distance from the figure: ,Q=+16e,q1=+4e,q2=-2e,d=140cm,θ1=43oandθ2=60o

02

Understanding the concept of the work done

We know that the work done by a body is given by the difference between the potential energies of the system. Thus, for initial potential energy as zero, as the particle brought from infinity, we can say the work is equal to the final potential energy.

Formula:

The potential energy of the system, U=kq1q2d

03

Calculation of the work done

After reading the question, and from the given figure,

W=ΔU=Uf-Ui=Uf-0=Uf

Thus, the total required work done is given using equation (i) as follows:

W=14πε0q1Q2d+q2Qd=9.0×1094×160.028-2×160.014×1.6×10-192=0J

Hence, the value of the work done is 0J.

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