I tried to correlate the angle made by the force F with the horizontal to the vertical angle made by the position vector about the centre. But with no improvement. IS there any alternate method?
@JohnRennie If we use the angle made with the horizontal, will that not vary non-uniformly? It varies faster near A and slower near B, am I right, sir?
That's where the problem arises. I haven't learnt 'curl' in much detail. I'm just using the classic, simple definitions of conservative and non-conservative force.
@JohnRennie I agree sir. But if we're not sure that the force is conservative, how can we make use of this method to assure that the work along AB is same as the work along the arc?
Ok sir. I can understand this. This is similar to opposite charges placed in the system with a constrain that one must move only along the curved path.
I understood this 'conservative' part based on electrostatic forces. But to fully understand, I think, I need to understand vector calculus. For the first part, I need to do the integration after our discussion.
Fun fact: I've studied about vectors as well as calculus. But I don't know vector calculus.
Could you recommend any good sources where I can get the basics of vector calculus? I'm seeing it more often now while reading answers on the main site.
Having found the force is conservative, as you told, the work along AB, the straight line is $120\sqrt 2$ which is correct. I need to do this using the formal (long) approach.
Is curl just a property of shape of the field rather than its magnitude sir? Here the force is uniform, but in our electrostatic analogy, it has an inverse square relationship.
Yes, it is a property of the shape not the value. Any field that has field lines forming loops will have a non-zero curl regardless of how the field varies along the field line.
