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Chapter 23: Q18P (page 680)

The electric field just above the surface of the charged conducting drum of a photocopying machine has a magnitude Eof2.3×105N/C . What is the surface charge density on the drum?

Short Answer

Expert verified

The surface charge density of the drum is 2.0×10-6C/m2.

Step by step solution

01

The given data

The magnitude of the electric field,E=2.3×105N/C

02

Understanding the concept of Gauss law-planar symmetry

Using the concept of the electric field of a conducting sheet, we can calculate the required surface charge density of the drum.

Formula:

The electric field of a conducting sheet, E=σε0 (1)

03

Calculation of the surface charge density

Using the given data in equation (1), we can get the value of the surface charge density of the drum such that,

σ=Eε0=2.3×105N/C8.85×10-12C2/N·m2=2.0×10-6C/m2

Hence, the required value of the density is 2.0×10-6C/m2.

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Most popular questions from this chapter

A thin-walled metal spherical shell has radius0.25cmand charge 2.88x104N/C. Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.

A surface has the area vectorA→=(2i^+3j^)m2. What is the flux of a uniform electric field through the area if the field is (a)E→=4i^N/Cand (b)E→=4j^N/C.

Water in an irrigation ditch of width w = 3.22mand depth d= 1.04mflows with a speed of 0.207 m/s. The mass flux of the flowing water through an imaginary surface is the product of the water’s density (1000 kg/m3) and its volume flux through that surface. Find the mass flux through the following imaginary surfaces:

(a) a surface of areawd, entirely in the water, perpendicular to the flow;

(b) a surface with area 3wd / 2, of which is in the water, perpendicular to the flow;

(c) a surface of area wd / 2,, entirely in the water, perpendicular to the flow;

(d) a surface of area wd, half in the water and half out, perpendicular to the flow;

(e) a surface of area wd, entirely in the water, with its normalfrom the direction of flow.

An electric field given by E=4.0i^-3.0(y2+2.0)j^, pierces a Gaussian cube of edge length 2.0mand positioned as shown in Fig. 23-7. (The magnitude Eis in Newton per coulomb and the position xis in meters.) What is the electric flux through the (a) top face, (b) bottom face, (c) left face, and (d) back face? (e) What is the net electric flux through the cube?

Fig. 23-31 shows a Gaussian surface in the shape of a cube with edge length 1.40m. What are (a) the net flux through the surface and (b) the net chargeqencenclosed by the surface if E→=3.00yj^+E0→with yin meters? What are (c)ϕand (d) qencif E→=-4.00i^+6.00+3.00yj^NC?
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