EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
16th Edition
ISBN: 8220100546716
Author: Katz
Publisher: CENGAGE L
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Chapter 24, Problem 16PQ

Figure P24.16 shows three charged particles arranged in the xy plane at the coordinates shown, with qA = qB = −3.30 nC and qC = 4.70 nC. What is the electric field due to these particles at the origin?

Chapter 24, Problem 16PQ, Figure P24.16 shows three charged particles arranged in the xy plane at the coordinates shown, with

FIGURE P24.16

Expert Solution & Answer
Check Mark
To determine

The electric field due to the particles at the origin.

Answer to Problem 16PQ

The electric field at the origin is E=(9331N/C)i^+(3719N/C)j^.

Explanation of Solution

Write the formula for the x component of the electric field due to charge qA at the origin.

  EAx=kqArA2cosθ

Here, EAx is the x component of the electric field due to charge qA, k is the coulomb’s constant, θ is the angle made by EA with x-axis, and rA is the distance of charge qA from origin.

Re-write the above equation by substituting expression for cosθ.

    EAx=kqAxArA3

Here, xA is the x component of the distance of qA from origin.

Similarly write the formula for the x component of the electric field due to qB.

    EBx=kqBxBrB3

Here, EBx is the x component of the electric field due to qB, rB is the distance of qB from origin, and xB is the x-component of the distance of qB from origin.

Write the formula for the x component of the electric field due to qC.

    ECx=kqCxCrC3

Here, ECx is the x component of the electric field due to qC, rC is the distance of qC from origin, and xC is the x-component of the distance of qC from origin.

Write the x component of the net electric field at origin.

    Ex=kqAxArA3+kqBxBrB3+kqCxCrC3                                                                          (I)

Similarly write the y component of the electric field at origin.

    Ey=kqAyArA3+kqByBrB3+kqCyCrC3                                                                         (II)

Here, Ey is the y component of the net electric field at origin, yA is the y component of distance of qA, yB is the y component of distance of qB, and yC is the y component of distance of qC.

Substitute 8.99×109Nm2/C2 for k, 3.30nC for qA, 3.30nC for qB, 4.70nC for qC, 7.60cm for xA, 7.60cm for xC, 0 for xB, (7.60cm)2+(3.50cm)2 for rA, (7.60cm)2+(3.50cm)2 for rC, 10cm for rB in equation (I).

Ex=(8.99×109Nm2/C2)(|(3.30nC)(7.60cm)((7.60cm)2+(3.50cm)2)3|+(3.30nC)(0)(10cm)3|(4.70nC)(7.60cm)((7.60cm)2+(3.50cm)2)3|)=(8.99×109Nm2/C2)(|(3.30×109C)(7.60×102m)((7.60×102m)2+(3.50×102m)2)3|+(3.30×109C)(0)(10×102m)3|(4.70×109C)(7.60×102m)((7.60×102m)2+(3.50×102m)2)3|)=3849N/C+0-5482N/C=9331N/C

Substitute 8.99×109Nm2/C2 for k, 3.30nC for qA, 3.30nC for qB, 4.70nC for qC, 3.50cm for yA, 3.50cm for yC, 10.0cm for yB, (7.60cm)2+(3.50cm)2 for rA, (7.60cm)2+(3.50cm)2 for rC, 10cm for rB in equation (II).

Ey=(8.99×109Nm2/C2)((3.30nC)(3.50cm)((7.60cm)2+(3.50cm)2)3|(3.30nC)(10.0cm)(10cm)3||(4.70nC)(3.50cm)((7.60cm)2+(3.50cm)2)3|)=(8.99×109Nm2/C2)((3.30×109C)(3.50×102m)((7.60×102m)2+(3.50×102m)2)3|(3.30×109C)(10.0×102m)(10×102m)3||(4.70×109C)(3.50×102m)((7.60×102m)2+(3.50×102m)2)3|)=1772N/C-2967N/C-2524N/C=-3719N/C

Conclusion:

The electric field at the origin is E=(9331N/C)i^+(3719N/C)j^.

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Chapter 24 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

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