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I have read in my text book that electric field is the space or region around a charge in which an electric test charge would experience an electric force, while intensity is the force per unit charge. What is the difference between both, aren't both same?

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  • $\begingroup$ High school textbooks tend to introduce lots of terms nobody else uses. There's no point in distinguishing "electric field", "electric field strength", and "electric field intensity". All that matters is the electric field. $\endgroup$
    – knzhou
    Dec 2, 2018 at 14:36
  • $\begingroup$ Your book seems to be quite clear: the field is a certain region. Something that has a volume. Intensity is a force per unit charge. A force has a magnitude and a direction. $\endgroup$
    – Jasper
    Dec 2, 2018 at 14:43
  • $\begingroup$ It's a little confusing when they say force per unit charge, I know they are referring to a test unit of charge say 1 electron. But the field is also generated by "unit" charges, say 10 electrons, so they should be clear that they are talking about the test charge unit and not the source charge which could be single of many units. $\endgroup$ Dec 2, 2018 at 15:03

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The electric field is a vector, a quantity that has both a magnitude and a direction. The electric field intensity is the magnitude of the vector.

For example, if we had an electric field vector which extended 1 unit in the x direction and 1 unit in the y direction, then its magnitude would be $\sqrt{1^2+1^2}=\sqrt{2}$ units.

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  • $\begingroup$ Is the word intensity a little misused here, usually when we talk of intensity (like light intensity) we are referring to the energy or power which is actually the square of the field..? $\endgroup$ Dec 19, 2018 at 21:28
  • $\begingroup$ @PhysicsDave Yes, usually the word used is "strength" rather than "intensity," but it's not like abuse of terminology doesn't happen all the time anyway. I take as my prime example the inconsistency of the term "magnetic field strength" (depending on the textbook, this can refer to either $\mathbf{B}$ or $\mathbf{H}$; in the latter case, $\mathbf{B}$ is usually, but not always, referred to as "magnetic induction"). $\endgroup$ Dec 19, 2018 at 22:54
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It's a little confusing when they say force per unit charge, I know they are referring to a test unit of charge say 1 electron. But the field is also generated by "unit" charges, say 10 electrons, so they should be clear that they are talking about the test charge unit and not the source charge which could be single of many units. –

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    $\begingroup$ This does not answer the question. It is a comment, and should be placed there. In fact, it is. I recommend that you delete this answer since your ideas are already published as a comment. $\endgroup$
    – garyp
    Dec 2, 2018 at 15:16
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The electric field acts in different directions. In each direction it acts with a certain strength. Lets say that it acts with $E_x$ in the $x$-direction, with $E_y$ in the $y$-direction, and with $E_z$ in the $z$-direction. The total electric field is now represented by \begin{equation} \boldsymbol E=\begin{pmatrix}E_x\\ E_y\\ E_z\end{pmatrix}. \end{equation}

The total field strength is now given by \begin{align} |\,\boldsymbol E\,|&=\sqrt{E_x^2+E_y^2+E_z^2} = E. \end{align}

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