A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of $$6\,mA$$ it produces a deflection of $$2^\circ$$, its figure of merit is close to:

The quantity that characterises a galvanometer is called its figure of merit. By definition, the figure of merit $$k$$ is the current required to produce one scale-division (or one degree) of deflection. In symbols we write

$$k \;=\; \frac{I}{\theta}$$

where $$I$$ is the current through the galvanometer and $$\theta$$ is the resulting deflection expressed in the same units (here, degrees).

We are told that a current of $$6\,\text{mA}$$ produces a deflection of $$2^\circ$$. First convert the current into amperes because the options are quoted in amperes per division:

$$I \;=\; 6\,\text{mA} \;=\; 6 \times 10^{-3}\,\text{A}$$

The deflection is already in degrees, so $$\theta = 2^\circ$$.

Now substitute these numbers into the formula for $$k$$:

$$k \;=\; \frac{I}{\theta} \;=\; \frac{6 \times 10^{-3}\,\text{A}}{2^\circ}$$

Carrying out the division step by step, we have

$$k \;=\; 3 \times 10^{-3}\,\text{A}\;/\;^\circ$$

This means that a current of $$3 \times 10^{-3}\,\text{A}$$ is needed for every one-degree deflection, which is precisely the quantity asked for.

Looking at the given options, we see that

Option D: $$3 \times 10^{-3}\,\text{A/div}$$

matches our calculated value.

Hence, the correct answer is Option D.