Chapter 24: Q27P (page 712)

Question: In Fig. 24-46, three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the three rods are, $Q_{1} = + 30 nC, Q_{2} = + 3.0 Q_{1} and Q_{3} = - 8.0 Q_{1}$ . What is the net electric potential at the origin due to the rods?

Short Answer

Expert verified

Answer:

The net electric potential at the origin due to the rods is +13.5 KV.

Step by step solution

The given data

The uniform charges on the three rods, $Q_{1} = + 30 nC, Q_{2} = + 90 nCand Q_{1} = - 240 nC$ .
The different radii are given as: $R_{3} = 0.04 m, R_{2} = 0.02 m, R_{1} = 0.01 m$

Understanding the concept of the electric potential

Using the concept of electric potential at a point due to many charges present in the system, we can get the required electric potential at the given point at a distance from the center of the y-axis.

Formula:

The electric potential at a point due to a charge, $V = \frac{1}{4 π ε_{0}} \frac{Q}{R}$ (i)

Calculation of the net electric potential

The net electric potential at the origin due to the charges present in the system is given using equation (i) as follows:

$V_{n e t} = V_{1} + V_{2} + V_{3} V_{n e t} = \frac{1}{4 π ε_{0}} [\frac{Q_{3}}{R_{3}} + \frac{Q_{2}}{R_{2}} + \frac{Q_{1}}{R_{1}}] = 9.0 \times 10^{9} \times Q_{1} [\frac{- 8}{0.04 m} + \frac{3}{0.02 m} + \frac{1}{0.01 m}] = 9.0 \times 10^{9} \times 30 \times 10^{- 9} [- 200 + 150 + 100] = + 1.35 \times 10^{4} V = + 13.5 kV$

Hence, the net potential is +13 .5 KV.

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Question: In Fig. 24-46, three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the three rods are, $Q_{1} = + 30 nC, Q_{2} = + 3.0 Q_{1} and Q_{3} = - 8.0 Q_{1}$ . What is the net electric potential at the origin due to the rods?

Short Answer

Step by step solution

The given data

Understanding the concept of the electric potential

Calculation of the net electric potential

One App. One Place for Learning.

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Question: In Fig. 24-46, three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the three rods are,Q1=+30nC,Q2=+3.0Q1andQ3=-8.0Q1. What is the net electric potential at the origin due to the rods?

Short Answer

Step by step solution

The given data

Understanding the concept of the electric potential

Calculation of the net electric potential

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Fields in Physics

Kinematics Physics

Atoms and Radioactivity

Physics of Motion

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

Question: In Fig. 24-46, three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the three rods are, $Q_{1} = + 30 nC, Q_{2} = + 3.0 Q_{1} and Q_{3} = - 8.0 Q_{1}$ . What is the net electric potential at the origin due to the rods?