- $3.00 \times 10^3 \textrm{ V}$
- $750 \textrm{ V}$

### Solution video

# OpenStax College Physics, Chapter 19, Problem 15 (Problems & Exercises)

### Calculator Screenshots

*d*and we ends up with

*V*equals

*E*times

*d*so that’s 7.5 times ten to the four volts per meter or newtons per coulomb if you prefer multiplied by four times ten to the minus two meters, separation that’s four centimetres that’s works out to three times ten to the three volts and if you were one centimetre from one of the plates then the potential difference between that position and the plate with zero potential will be the electric field times that separation from the plate pf zero potential and that’s 7.50 times ten to the four volts per meter times one centimetre which is one times ten to the minus two meters giving us 750 volts potential difference from that position to the plate with zero potential.

## Comments

My professor gave us the equation deltaV=-E*delta d, is this the same as V=Ed? I thought i was supposed to use the negative sign, so my answer ended up being wrong

Hi mesmes, in a question like this "what is the potential difference" it's common to not care about the negative sign. Strictly speaking $\Delta V = =E \delta d$ is best, but the $\Delta$ is understood in this context. We're always measuring differences. Voltage, like any mechanical potential energy, is always a difference compared to something else. In this case it's the difference between the two plates.

As a thought experiment to understand where the negative comes from, electric field causes the kinetic energy of an initially stationary positive test charge to increase by accelerating it in the direction of the field. This increase in kinetic energy comes with an equal reduction in potential energy. Electric field therefore is pointing in the direction of decreasing potential energy. The negative sign is meant to indicate this.

Can someone explain the exponents to me?