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Chapter 24, Problem 51PQ

Figure P24.51 shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm.

a. What is the electric field at the location of the sphere with charge +2.00 nC?

b. What is the total electric force exerted on the sphere with charge +2.00 nC by the other three spheres?

Chapter 24, Problem 51PQ, Figure P24.51 shows four small charged spheres arranged at the corners of a square with side d =

FIGURE P24.51

(a)

Expert Solution
Check Mark
To determine

The electric field at the location of the sphere with charge +2.00nC.

Answer to Problem 51PQ

The electric field at the location of the sphere with charge +2.00nC is (347i^635j^)N/C.

Explanation of Solution

Sketch the diagram showing the electric fields and position vectors of the charges.

Bundle: Physics For Scientists And Engineers: Foundations And Connections, Volume 2, Loose-leaf Version + Webassign Printed Access Card For Katz's ... And Connections, Single-term Courses, Chapter 24, Problem 51PQ

Write the equation for the electric field of a charged particle.

E=kqr2r^ (I)

Here, EE is the electric field of a charged particle, k is the Coulomb’s constant, r is the distance and r^ is the surface unit vector in the direction for r.

Use equation (I) to find the equation for the sum of the electric field at the location of the sphere with charge +2.00nC.

E=kq1r12r^1+kq3r32r^3+kq4r42r^4 (II)

Here, q1 is the is the first charge, q4 is the is the third charge, q3 is the is the third charge, r1 is the distance of the first charge to the +2.00nC charge, r3 is the distance of the third charge to the +2.00nC charge, r4 is the distance of the fourth charge to the +2.00nC charge, r^1 is the unit vector in the direction of r1, r^3 is the unit vector in the direction of r3 and r^4 is the unit vector in the direction of r4.

Conclusion:

Substitute 8.99×109Nm2/C2 for k, 1.00nC for q1, 4.00nC for q3 and 3.00nC for q4, d for r1, 2d for r3, d for r4, i^ for r^1, (cos45.0i^+sin45.0j^) for r^3 and j^ for r^4 in equation (II) to find E.

E=k[1.00nCd2i^4.00nC(2d)2(cos45.0i^+sin45.0j^)3.00nCd2j^]=k[(1.00nC)(109C1nC)d2i^(4.00nC)(109C1nC)(2d)2(cos45.0i^+sin45.0j^)(3.00nC)(109C1nC)d2j^]=8.99×109Nm2/C2((25.0cm)(102m1cm))2(109C)[(12cos45.0°)i^+j^]=(347i^635j^)N/C

Thus, the electric field at the location of the sphere with charge +2.00nC is (347i^635j^)N/C.

(b)

Expert Solution
Check Mark
To determine

The total electric forceon the sphere with charge +2.00nC.

Answer to Problem 51PQ

The total electric force on the sphere with charge +2.00nC is (6.94×107i^1.27×106j^)N

Explanation of Solution

Write the equation for the electric force.

F=qE (III)

Here, F is the electric force.

Conclusion:

Substitute 2.00nC for q and (347i^635j^)N/C for E in equation (III) to find F.

F=(2.00nC)((347i^635j^)N/C)=((2.00nC)(109C1nC))((347i^635j^)N/C)=(6.94×107i^1.27×106j^)N

Thus, the total electric force on the sphere with charge +2.00nC is (6.94×107i^1.27×106j^)N.

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Chapter 24 Solutions

Bundle: Physics For Scientists And Engineers: Foundations And Connections, Volume 2, Loose-leaf Version + Webassign Printed Access Card For Katz's ... And Connections, Single-term Courses

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