Explanation 1) Concept Work done by an external agent to move a particle of charge through an electric field is equal to the potential energy of the system. 2) Formulae i. Electric potential energy is U = q V ii. Electric potential at a point due to a point charge q V = k q r Where k- 1 4 π ε o c a l l e d Coulomb’s constant which is equal to 8.99 x 10 9 N . m 2 C 2 r- is the distance of the point from the charge iii. For two particles at separation r , the potential energy is U= k q 1 q 2 r 3) Given Charge on particle 1, q 1 =-2e Charge on particle 2, q 2 =+2e Charge on particle 3, q 3 =+2e Distance of point P from particle 1, d 1 =4.00 m Distance of point P from particle 1, d 2 =2.00 m V=0 at infinity 4) Calculations (d) Applying superposition of potential, we get Potential at point P V P = 2 e 4 π ε 0 d + - 2 e 4 π ε 0 2 d = e 4 π ε 0 d Where e= 1.6 × 1 0 - 19 C Plugging all the values gives us V P = ( 8.99 × 1 0 9 N . m 2 / C 2 ) ( 1.6 × 1 0 - 19 C ) 2.00 m = 7.192 × 1 0 - 10 V V at P is 7.192 × 1 0 - 10 V (b) Since movable particle's contribution of the potential energy when it is infinity is zero, and its contribution to U system when it is at P is, U = q V P Work done, W = U system Plugging the values of q and V P U = 2 1

FUND. OF PHYSICS (LL)-W/WILEY+NEXTGEN(2)

11th Edition

ISBN: 9781119787235

Author: Halliday

Publisher: WILEY

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Chapter 24, Problem 83P

To determine

To find:

(a) V at point P

(b) Amount of work required to bring a particle of charge q₃ from infinity to P

(c) the potential energy of the three-particle system

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Chapter 24, Problem 82P

Chapter 24, Problem 84P

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Chapter 24 Solutions

FUND. OF PHYSICS (LL)-W/WILEY+NEXTGEN(2)

Ch. 24 - Figure 24-24 shows eight particles that form a...Ch. 24 - Figure 24-25 shows three sets of cross sections of...Ch. 24 - Figure 24-26 shows four pairs of charged...Ch. 24 - Figure 24-27 gives the electric potential V as a...Ch. 24 - Figure 24-28 shows three paths along which we can...Ch. 24 - Figure 24-29 shows four arrangement? of charged...Ch. 24 - Figure 24-30 shows a system of three charged...Ch. 24 - In the situation of Question 7, is the work done...Ch. 24 - Figure 24-26 shows four pairs of charged particles...Ch. 24 - a In Fig. 24-31a, what is the potential at point P...

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(a) V at point P (b) Amount of work required to bring a particle of charge q 3 from infinity to P (c) the potential energy of the three-particle system

To find: (a) V at point P (b) Amount of work required to bring a particle of charge q3 from infinity to P (c) the potential energy of the three-particle system

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Chapter 24 Solutions

To find:

(a) V at point P

(b) Amount of work required to bring a particle of charge q₃ from infinity to P

(c) the potential energy of the three-particle system