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Chapter 11: Problem 1625

Two positive point charges of \(12 \mu \mathrm{c}\) and \(8 \mu \mathrm{c}\) are placed \(10 \mathrm{~cm}\) apart in air. The work done to bring them $4 \mathrm{~cm}$ closer is (A) Zero (B) \(4.8 \mathrm{~J}\) (C) \(3.5 \mathrm{~J}\) (D) \(-5.8 \mathrm{~J}\)

Short Answer

Expert verified
The work done to bring the two point charges $4\mathrm{~cm}$ closer is approximately \(5.76 \mathrm{J}\). The given options contain an error, as none of them match the calculated result.

Step by step solution

01

Identify given values and the formula to use

The given values are: \(Q_1 = 12 \mu \mathrm{C} = 12 \times 10^{-6} \mathrm{C}\), \(Q_2 = 8 \mu \mathrm{C} = 8 \times 10^{-6} \mathrm{C}\), initial distance \(r_1 = 10 \mathrm{cm} = 0.1 \mathrm{m}\), and final distance \(r_2 = 6 \mathrm{cm} = 0.06 \mathrm{m}\). We will use the formula for the electrostatic potential energy: \[ U = \frac{kQ_1Q_2}{r} \]
02

Calculate the initial potential energy

Find the initial potential energy by plugging in the values into the formula: \[ U_1 = \frac{kQ_1Q_2}{r_1} \] \[ U_1 = \frac{(9 \times 10^9 \mathrm{Nm^2C^{-2}})(12 \times 10^{-6} \mathrm{C})(8 \times 10^{-6} \mathrm{C})}{0.1 \mathrm{m}} \] \[ U_1 = 8.64 \mathrm{J} \]
03

Calculate the final potential energy

Find the final potential energy by plugging in the values into the formula: \[ U_2 = \frac{kQ_1Q_2}{r_2} \] \[ U_2 = \frac{(9 \times 10^9 \mathrm{Nm^2C^{-2}})(12 \times 10^{-6} \mathrm{C})(8 \times 10^{-6} \mathrm{C})}{0.06 \mathrm{m}} \] \[ U_2 = 14.4 \mathrm{J} \]
04

Calculate the work done

Find the work done by calculating the difference between the final and initial potential energies: \[ W = U_2 - U_1 \] \[ W = 14.4 \mathrm{J} - 8.64 \mathrm{J} \] \[ W = 5.76 \mathrm{J} \] Since the work done is not equal to the given options, we can conclude that the exercise has an error in its options. The correct answer should be approximately \(5.76 \mathrm{J}\).

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Most popular questions from this chapter

Two parallel plate air capacitors have their plate areas 100 and $500 \mathrm{~cm}^{2}$ respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is \(0.5 \mathrm{~mm}\), what is the distance between the plates of the second capacitor ? (A) \(0.25 \mathrm{~cm}\) (B) \(0.50 \mathrm{~cm}\) (C) \(0.75 \mathrm{~cm}\) (D) \(1 \mathrm{~cm}\)

Two point charges \(100 \mu \mathrm{c}\) and \(5 \mu \mathrm{c}\) are placed at points \(\mathrm{A}\) and \(B\) respectively with \(A B=40 \mathrm{~cm}\). The work done by external force in displacing the charge \(5 \mu \mathrm{c}\) from \(\mathrm{B}\) to \(\mathrm{C}\) where \(\mathrm{BC}=30 \mathrm{~cm}\), angle \(\mathrm{ABC}=(\pi / 2)\) and \(\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\) \(=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{c}^{2}\). (A) \(9 \mathrm{~J}\) (B) \((9 / 25) \mathrm{J}\) (C) \((81 / 20) \mathrm{J}\) (D) \(-(9 / 4) \mathrm{J}\)

If an electron moves from rest from a point at which potential is 50 volt, to another point at which potential is 70 volt, then its kinetic energy in the final state will be \(\ldots .\) (A) \(1 \mathrm{~N}\) (B) \(3.2 \times 10^{-18} \mathrm{~J}\) (C) \(3.2 \times 10^{-10} \mathrm{~J}\) (D) 1 dyne

An electric circuit requires a total capacitance of \(2 \mu \mathrm{F}\) across a potential of \(1000 \mathrm{~V}\). Large number of \(1 \mu \mathrm{F}\) capacitances are available each of which would breakdown if the potential is more then \(350 \mathrm{~V}\). How many capacitances are required to make the circuit? (A) 24 (B) 12 (C) 20 (D) 18

If a charged spherical conductor of radius \(10 \mathrm{~cm}\) has potential \(\mathrm{v}\) at a point distant \(5 \mathrm{~cm}\) from its centre, then the potential at a point distant \(15 \mathrm{~cm}\) from the centre will be $\ldots . .$ (A) \((1 / 3) \mathrm{V}\) (B) \((3 / 2) \mathrm{V}\) (C) \(3 \mathrm{~V}\) (D) \((2 / 3) \mathrm{V}\)
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