B

A potentiometer is used to measure the potential difference (voltage) by balancing it against a known voltage. The potential gradient is defined as the potential difference per unit length of the wire.

Step 1: The potential gradient (k) is given by the formula:
$$ k = \frac{V}{L} $$
where V is the potential difference across the potentiometer wire and L is the length of the wire.

Step 2: If the length of the potentiometer wire (L) is increased, for a constant voltage (V), the potential gradient (k) will decrease. This is because the same voltage is distributed over a longer length of wire.

Therefore, if the length of the potentiometer wire is kept larger, the value of potential gradient will decrease.

Hence, the correct answer is Option B.