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Chapter 23: Problem 2

How does the energy density at a certain distance from a negative point charge compare with the energy density at the same distance from a positive point charge of equal magnitude?

Short Answer

Expert verified
The energy density at a certain distance from a point charge is the same, regardless of whether the charge is positive or negative. This is because the energy density depends on the square of the electric field's magnitude, rather than the sign of the charge that generates the field.

Step by step solution

01

Understanding electric field and energy density

An electric field is generated by charges, such as a positive or negative point charge. The field extends in all directions from the charge and its strength lessens with distance. The energy stored in this electric field is represented by the energy density, which in the case of an electric field, is given by \(U = \frac{1}{2} 蔚_0 E^2\), where \(蔚_0\) is the permittivity of free space and \(E\) is the electric field's magnitude.
02

Comparing energy densities

The energy density depends on the square of the electric field's magnitude and the permittivity of the free space, but it does not depend on the sign of the charge that creates the field. Since the charges in question are of equal magnitude, and we are considering the same distance in each case, the magnitude of the electric fields created would be the same.
03

Conclusion

Both a negative and a positive point charge of equal magnitude at the same distance will therefore have the same energy density. The fact that one of the charges is negative does not affect this energy density as it is not dependent on the charge's polarity.

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Most popular questions from this chapter

An uncharged capacitor has parallel plates \(5.0 \mathrm{cm}\) on a side, spaced \(1.2 \mathrm{mm}\) apart. (a) How much work is required to transfer \(7.2 \mu \mathrm{C}\) from one plate to the other? (b) How much work is required to transfer an additional \(7.2 \mu \mathrm{C} ?\)

A transmission line consists of two parallel wires, of radius \(a\) and separation \(b,\) carrying uniform line charge densities \(\pm \lambda,\) respectively. With \(a \ll b\), their electric field is the superposition of the fields from two long straight lines of charge. Find the capacitance per unit length for this transmission line.

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