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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

An electron is projected with an initial speed of 3.2脳105m/sdirectly toward a proton that is fixed in place. If the electron is initially a great distance from the proton, at what distance from the proton is the speed of the electron instantaneously equal to twice the initial value?

A hollow metal sphere has a potential of +400Vwith respect to ground (defined to be atV=0 ) and a charge of 5.0脳10鈭�9C. Find the electric potential at the centre of the sphere.

In Fig. 24-70, point P is at the center of the rectangle. With V=0at infinity, q1=5.00fC , q2=2.00fC , q3=3.00fC, andd=2.54cm, what is the net electric potential at P due to the six charged particles?

The chocolate crumb mystery. This story begins with Problem 60 in Chapter 23. (a) From the answer to part (a) of that problem, find an expression for the electric potential as a function of the radial distance r from the center of the pipe. (The electric potential is zero on the grounded pipe wall.) (b) For the typical volume charge density 蚁=-1.1脳10-3C/m3 , what is the difference in the electric potential between the pipe鈥檚 center and its inside wall? (The story continues with Problem 60 in Chapter 25.)

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(a) only the two up quarks and

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