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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,Q1=+30nC,Q2=+3.0Q1andQ3=-8.0Q1. 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

01

The given data

  1. The uniform charges on the three rods,Q1=+30nC,Q2=+90nCandQ1=-240nC.
  2. The different radii are given as:R3=0.04m,R2=0.02m,R1=0.01m
02

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=14蟺蔚0QR (i)

03

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:

Vnet=V1+V2+V3Vnet=14蟺蔚0Q3R3+Q2R2+Q1R1=9.0脳109脳Q1-80.04m+30.02m+10.01m=9.0脳109脳30脳10-9-200+150+100=+1.35脳104V=+13.5kV

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

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Most popular questions from this chapter

Question: In Fig. 24-53, seven charged particles are fixed in place to form a square with an edge length of 4.0 cm. How much work must we do to bring a particle of charge +6Einitially at rest from an infinite distance to the center of the square?

What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius 0.15 mwhose potential is 200 V(with V = 0at infinity)?

Electron in a well. Figure 24- 65 shows electric potential V along an x-axis. The scale of the vertical axis is set byVs=8.0V . An electron is to be released at x=4.5cmwith initial kinetic energy 3.00eV. (a) If it is initially moving in the negative direction of the axis, does it reach a turning point (if so, what is the x coordinate of that point) or does it escape from the plotted region (if so, what is its speed atrole="math" localid="1662990552191" x=0 )? (b) If it is initially moving in the positive direction of the axis, does it reach a turning point (if so, what is the x coordinate of that point) or does it escape from the plotted region (if so, what is its speed at x=7.0cm)? What are the (c) magnitude F and (d) direction (positive or negative direction of the x axis) of the electric force on the electron if the electron moves just to the left ofx=4.0cm ? What are (e) F and (f) the direction if it moves just to the right ofx=5.0cm ?

A positron (charge +e, mass equal to the electron mass) is moving at 1.0x107 m/sin the positive direction of an xaxis when, at x=0, it encounters an electric field directed along the xaxis. The electric potential Vassociated with the field is given in Fig. 24-57. The scale of the vertical axis is set by Vs=500.0 V. (a) Does the positron emerge from the field at x=0(which means its motion is reversed) or at x=0.50 m(which means its motion is not reversed)? (b) What is its speed when it emerges?

In the situation of Question 7, is the work done by your force positive, negative, or zero if the particle is moved (a) from Ato B, (b) from Ato C, and (c) from Bto D? (d) Rank those moves according to the magnitude of the work done by your force, greatest first.
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