The value of \(\displaystyle\int_{A}^{B}(\bar{r} \times d\bar{r})\) from A(a, 0, 0) to B(a, 0, 2πb) along \(\bar{r}\) = (a cos t) \(\hat{i}\) + (a sin t) \(\hat{j}\) + bt \(\hat{k}\) is
1
πa (b\(\hat{j}\) + a\(\hat{k}\))
2
2πa (a\(\hat{i}\) + b\(\hat{j}\) + ab\(\hat{k}\))
3
2πa (a\(\hat{j}\) + b\(\hat{k}\))
4
2πa (b\(\hat{j}\) + a\(\hat{k}\))