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Chapter 24: Q86P (page 716)

Figure 24-68 shows a hemisphere with a charge of 4.00渭颁 distributed uniformly through its volume. The hemisphere lies on an xy plane the way half a grapefruit might lie face down on a kitchen table. Point P is located on the plane, along a radial line from the hemisphere鈥檚 center of curvature, at radial distance15cm .What is the electric potential at point P due to the hemisphere?

Short Answer

Expert verified

The electric potential at point P isV=0.24MV

Step by step solution

01

Step 1: Given data:

The charge on the hemisphere,q=4.0渭颁=4.0脳10鈭�6C.

The radius of the curvature, R=15cm=0.15m.

02

Determining the concept:

The electric potential at point P will be the same as on its surface because the charges are uniformly distributed.

Formula:

The potential is define by,

V=14蟺蔚o鈰�qR=kqR

Here, 蔚0 is the permittivity of free space, q is the electron charge, and R is the distance, and k is the Coulomb鈥檚 constant having a value 9脳109Nm2/C2.

03

Determining the electric potential:

Write the equation for the potential as below.

V=k鈰�qR

Substitute known values in the above equation.

V=(9脳109Nm2/C2)脳4.0脳10鈭�6C0.15m=2.4脳105V=0.24MV

Hence, the electric potential is 0.24MV.

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Most popular questions from this chapter

A solid conducting sphere of radius 3.0cmhas a charge of30nc distributed uniformly over its surface. Let A be a point1.0cm from the center of the sphere,S be a point on the surface of the sphere, and Bbe a point5.0cm from the center of the sphere.What are the electricpotential differences

(a) VS鈭�VBand

(b) VA鈭�VB?

Question: In Fig. 24-43, a plastic rod having a uniformly distributed charge Q = -25.6pChas been bent into a circular arc of radius R = 3.71 cmand central angle蠒=120掳. With V = 0at infinity, what is the electric potential at P, the center of curvature of the rod?

Two charged, parallel, flat conducting surfaces are spaced d=1.00cmapart and produce a potential difference螖痴=625V between them. An electron is projected from one surface directly toward the second. What is the initial speed of the electron if it stops just at the second surface?

Two tiny metal spheres Aand B,massmA=5.00gandmB=10.00g, have equal positive chargeq=5.00渭颁. The spheres are connected by a mass less non-conducting string of length d=1.00 m, which is much greater than the radii of the spheres. (a) What is the electric potential energy of the system? (b) Suppose you cut the string. At that instant, what is the acceleration of each sphere? (c) A long time after you cut the string, what is the speed of each sphere?

In Fig. 24-40, particles with the chargesq1 = +5e and q2 = -15eare fixed in place with a separation of d = 24.0 cm. With electric potential defined to be V = 0at infinity, what are the finite (a) positive and (b) negative values of xat which the net electric potential on the x axis is zero?
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