Chapter 24: Q50P (page 713)

Question: In Fig. 24-54, how much work must we do to bring a particle, of charge $Q = + 16 e$ and initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of charges $q_{1} = + 4 E a n d q_{2} = - q_{1} / 2$ ? Distance, $d = 1.40 cm, θ_{1} = 43 ° a n d θ_{2} = 60 °$

Short Answer

Expert verified

Answer:

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

Step by step solution

The given data

The given values of charges and distance from the figure: , ${Q=+16e,q}_{1} = + 4 e, q_{2} = - 2 e, d =140 c m, θ_{1} = 43^{o} a n d θ_{2} = 60^{o}$

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, $U = \frac{k q_{1} q_{2}}{d}$

Calculation of the work done

After reading the question, and from the given figure,

$W = Δ U = U_{f} - U_{i} = U_{f} - 0 = U_{f}$

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

$W = \frac{1}{4 π ε_{0}} [\frac{q_{1} Q}{2 d} + \frac{q_{2} Q}{d}] = 9.0 \times 10^{9} [\frac{4 \times 16}{0.028} - \frac{2 \times 16}{0.014}] \times {(1.6 \times 10^{- 19})}^{2} = 0 J$

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

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Short Answer

Step by step solution

The given data

Understanding the concept of the work done

Calculation of the work done

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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

Step by step solution

The given data

Understanding the concept of the work done

Calculation of the work done

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Conservation of Energy and Momentum

Electrostatics

Electromagnetism

Geometrical and Physical Optics

Engineering Physics

Study anywhere. Anytime. Across all devices.