Question
The electric field strength between two parallel conducting plates separated by 4.00 cm is 7.50×104 V/m7.50 \times 10^4 \textrm{ V/m}. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?
Question by OpenStax is licensed under CC BY 4.0
Final Answer
  1. 3.00×103 V3.00 \times 10^3 \textrm{ V}
  2. 750 V750 \textrm{ V}

Solution video

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

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Video Transcript
This is College Physics Answers with Shaun Dychko. Electric field is the potential difference between two large parallel plates divided by the separation between them and we can solve for potential difference by multiplying both sides by separation 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 ΔV==Eδd\Delta V = =E \delta d is best, but the Δ\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?