Coulomb's law says:
$$F = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{Q_t . Q_s}{{r_{st}}^2}$$
Just consider the test charge as unity. We are left with,
Just consider the test charge as unity. We are left with,
$$F = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{ Q_s}{{r_{st}}^2}$$
Making a slight change in notation ( replacing F with E ) we get,
$$E = \dfrac{1}{4\pi{\epsilon_0}}. \dfrac{ Q_s}{{r_{st}}^2}$$
Conclusion: Mathematically speaking, this is what we call definition of "Electric field".
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