A long hollow conducting cylinder A of radius $R_1$ is kept inside another long hollow conducting cylinder B of radius $R_2>R_1$. Initially cylinders A and B carry no charge. Which of the following statements is true?
1. When a charge density is given to the outer cylinder B, a potential difference appears between cylinders A and B.
2. When a charge density is given to the inner cylinder A, a potential difference appears between cylinders A and B;
3. When the same charge density is given to both A and B, no potential difference appears between them.