The bulb will get brighter
It doesn't matter where the bulb is in respect to the battery, as long as the circuit is complete, the bulb will light up.
When you move a bulb closer to the battery in a circuit, it will receive more electrical energy as the resistance decreases. This will cause the bulb to shine brighter due to the increased flow of electrical current passing through it.
Disconnecting a wire from a battery would break the circuit. If the battery was powering a bulb, the lamp would go out.
Close circuit is a complete circuit of battery wire bulb and a switch
In a simple circuit with a battery and a light bulb, the battery provides electrical energy that flows through the wires to the light bulb. The electrical energy causes the filament in the light bulb to heat up and emit light. This process continues as long as the circuit remains closed and the battery has power.
Circuit
When a battery is connected to a light bulb, the electrical current flows from the battery through the wire, causing the filament in the light bulb to heat up and emit light. The battery acts as a power source, providing the necessary voltage and current to illuminate the bulb.
series
You can use a circuit.
If you connect the circuit properly the bulb should light up. That means attaching the left side of the battery to the right side of the bulb using a wire and attaching the right side of the battery to the left side of the bulb. If you do that the your bulb should turn on. If it doesn't then try changing the battery or the bulb.
What needs to be complete is the circuit from the battery to the bulb, then the other wire from the bulb to the other side of the battery.If it is from an outlet rather than a battery, the circuit starts and finishes with the live and neutral pins at the outlet.
The whole circuit fails - because the action of the bulb blowing cuts the circuit.