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Chapter 21: Q4Q (page 897)

Based on its definition as electric flux per unit volume, what are the units of the divergence of electric field.

Short Answer

Expert verified

The unit of divergence of electric field is N·m/C.

Step by step solution

01

Conceptual Explanation

The divergence of electric field at any point is the effect of the charge density in a medium

02

Formula of divergence of electric field

The electric flux of enclosed surface is given as:

ϕ=Qε0......1

Here, Q is the enclosed charge and its units is Coulomb (C) and ε0is the permittivity of free space and its unit is C2/N·m2 so the unit of electric flux is N·m2/C

The divergence of the electric field is given as:

∇·E=ϕV......1

03

Determination of unit of divergence of electric field

Substitute units of electric flux and volume in the equation (1).

∇·E=N·m2/Cm3∇·E=N·m/C

Therefore, the unit of divergence of electric field on the basis of electric flux per unit volume is N·m/C.

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Most popular questions from this chapter

The center of a thin paper cube in outer space is located at the origin. Each edge is 10 cm long. The only other objects in the neighborhood are some small charged particles whose charges and position at this instant are following: +9 nC at (4,2,-3) cm, -6 nC at (1,-3,2) cm, +7 nC at (15,0,4) cm, +4 nC at (-1,3,2) cm and -3 nC at (-2,12,-3) cm. The electric flux on the five of the six faces of the cube totals 564 V m. What is the flux on the other face?

In chapter 15 we calculated the electric field at a location on the axis of a uniformly charged ring. Without doing all those calculations explain why we can’t use Gauss law to determine the electric field at that location.

In Figure 21.15 the magnitude of the electric field is 1000 V/m, and the field is at an angle of 30oto the outward-going normal. What is the flux on the small rectangle whose dimensions are 1 mmby2 mm ?

The electric field has been measured to be vertically upward everywhere on the surface of a box 30 cm long, 4 cm high and 3 cm deep as shown in Figure 21.64. All over the bottom of the box E1=1500V/m , all over the sides E2=1000V/mand all over the top E3=600V/m. What can you conclude about the contents of the box. Include a numerical result.

Explain why you are safe and unaffected inside a car that is struck by lightning. Also explain why it might not be safe to step out of the car just after the lightning strike, with one foot in the car and one on the ground (Note that it is current that kills;, rather a small current passing through the region of the heart can be fatal.)
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