Physics

Problem

(a) Write the vector form of Coulomb’s law for the force on charge

q_{2}

due to charge

q_{1}

, clearly identifying the meanings of

\mathbf r_{12}

and

\hat{\mathbf r}_{12}

. (b) Prove that the unit vector

\hat{\mathbf r}_{12}

is dimensionless whereas

r_{12}

carries the dimension of length. (c) Using dimensional analysis only, obtain the dimensions and the SI units of the electrostatic constant

k

appearing in Coulomb’s law. (d) If the law of force were hypothetically proportional to

1/r^{3}

instead of

1/r^{2}

, show how the dimensions of the new constant would alter and comment on the physical implication of such a change. a. (a) Statement of vector law b. (b) Dimensional nature of

\hat{\mathbf r}

and

r

c. (c) Dimensions and units of

k

d. (d) Consequence of a

1/r^{3}

dependence

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