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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

Along the path shown in Figure 21.46 the magnetic field is measured and is found to be uniform in magnitude and always tangent to the circular path. If the radius of the path is 3 cmand Balong the path is 1.3×10-6 T, what are magnitude and direction of the current enclosed by the path?

Figure 21.61 shows disk shaped region of radius of 2 cm on which there is a uniform electric field of magnitude 300 V/m at an angle of 300 to the plane of the disk. Assume that points upward in +y direction. Calculate the electric flux on the disk, and include the correct units.

The electric field on a closed surface is due to all the charges in the universe, including the charges outside the closed surface. Explain why the total flux nevertheless proportional only to the charges that are inside the surface, with no apparent influence of the charges outside.

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.)

Question: A negative point charge –Q is at the center of a hollow insulting spherical shell, which has an inner radius R1 and an outer radius R2. There is a total charge of +3Q spread uniformly throughout volume of insulating shell, not just on its surface. Determine the electric field for (a) r<R1 (b) R1<r<R2 (c) R2<r.
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