Explain point charges and expush the equation for electrical potential of a point charge. Distinguish between electric potential and also electrical field. Determine the electrical potential of a point charge offered charge and also distance.

You are watching: Find the potential at point a.

Point charges, such as electrons, are among the standard structure blocks of matter. In addition, spherical charge distributions (choose on a steel sphere) develop external electrical areas specifically favor a point charge. The electric potential because of a allude charge is, thus, a case we need to think about. Using calculus to find the work-related necessary to relocate a test charge (q) from a large distance ameans to a distance of (r) from a suggest charge (Q), and noting the link between work-related and also potential ((W=-qDelta V)), we deserve to specify the electrical potential (V) of a suggest charge:

definition: ELECTRIC POTENTIAL (V) OF A POINT CHARGE

The electrical potential (V) of a allude charge is offered by

wbelow (k) is a constant equal to (9.0 imes 10^9, mathrmNcdot mathrmm^2/C^2.)

The potential at infinity is liked to be zero. Thus (V) for a allude charge decreases through distance, whereas (mathbfE) for a suggest charge decreases with distance squared:

Respeak to that the electrical potential (V) is a scalar and also has actually no direction, whereas the electrical field (mathbfE) is a vector. To find the voltage due to a combination of suggest charges, you add the individual voltages as numbers. To uncover the full electric area, you must include the individual areas as vectors, taking magnitude and also direction right into account. This is regular with the fact that (V) is very closely linked through energy, a scalar, whereas (mathbfE) is very closely linked with pressure, a vector.

Example (PageIndex2): What Is the Excess Charge on a Van de Graaff Generator

A demonstration Van de Graaff generator has a 25.0 cm diameter metal spright here that produces a voltage of 100 kV near its surface. (Figure (PageIndex1)) What excess charge lives on the sphere? (Assume that each numerical worth here is shown through 3 significant figures.)

Figure (PageIndex1): The voltage of this demonstration Van de Graaff generator is measured in between the charged spbelow and ground. Earth’s potential is taken to be zero as a reference. The potential of the charged conducting sphere is the exact same as that of an equal suggest charge at its center.

Strategy

The potential on the surface will be the exact same as that of a suggest charge at the center of the spbelow, 12.5 cm away. (The radius of the spbelow is 12.5 cm.) We deserve to therefore recognize the excess charge utilizing Equation efeq1.

Solution

Solving for (Q) and also entering recognized worths gives

< eginalign* Q &=dfracrVk \<5pt> &= dfrac(0.125 ,mathrmm)(100 imes 10^3, mathrmV)8.99 imes 10^9, mathrmNcdot m^2/C^2 \<5pt> &= 1.39 imes 10^-6 ,mathrmC \<5pt> &= 1.39, mathrmmu C.endalign*>

Discussion

This is a fairly small charge, yet it produces a rather huge voltage. We have one more indication below that it is challenging to store isolated charges.

See more: Which Depends On Location Weight Or Mass And Weight, What Is The Difference Between Weight And Mass

## Summary

Electric potential of a point charge is (V=kQ/r). Electric potential is a scalar, and electric field is a vector. Addition of volteras as numbers offers the voltage because of a mix of allude charges, whereas addition of individual fields as vectors gives the total electrical area.