in my previous solution, I made a huge mistake. apologies for that. Here I have proven what you had asked. Doubts will be entertained. Not replying to comment would never help you....
solenoidal vectors: The vectors whose curl is zero. here you are asking to find the curl of gradient. but curl of gradient is always zero. In the below proof you can take gradient ...
it's because.....we know divergence simply means flux and when it's 0 means incoming flux = outgoing flux. means nothing inside. and solenoid has nothing inside that's why we calle...