This is a medical emergency!
A vet must make an x-ray of the stomach as soon as possible to verify whether or not the dog actually swallowed the battery. If he did indeed, the battery must be removed as soon as possible by a means the vet chooses. If the battery is intact, vomitting might be the easiest solution, but if the battery is punctured, it may cause even more damaged if vomitting is unducedinduced.
The stomach acid corrodes the outer layer of the battery, which then releases it's toxic chemicals into the stomach. That can cause chemical burns and tissue death anywhere from the mouth, to the esophagus, intestines and anus. Even if the battery wasn't punctured and passed through the stomach intact, it may still block the intestine and cause an incredibly painful intestinal obstruction that is lethal if untreated.
You should watch out for symptoms like:
- reluctance to eat or drink
- drooling
- red or grey spots in the dogs mouth
- bad breath
- vomitting
- diarheadiarrhea
- Lethargylethargy
As a first aid measure you should feed your dog a very bland diet of plain cookescooked chicken, rice or pasta (without added salt) and offer them some milk or cottage cheese.
For more information please read:
What should I do if my dog eats a battery? by Animal Emergency Center
The Dangers of Batteries and Your Pets: What You Should Know by the American Society for the Prevention of Cruelty to Animals (ASPCA)
Dogs & Batteries – More Dangerous Than You Might Think by Preventive Vet