vector calculus problems

[PG1995]

Thanks a lot.

The vector function in question is spherically symmetric and always points radially outward. Hence, there is no rotation or vortex in the field and curl is always zero in that case.

Let's forget spherical coordinates for a moment. Do you think it's apparent that curl has to be zero? I had thought that the author was too abrupt in stating the final answer. Please let me know. Thanks.

Regards
PG

PS: If you have time then please give this post a look. It looks MrAl is offline now.

 

[steveB]

I had thought that the author was too abrupt in stating the final answer. Please let me know.

It's pretty clear that each component off the vector is zero at the point the author says the answer is zero. Look at it again closely. Each component is written as one term minus another terms, but in each case the two terms are equal in magnitude, hence they subtract to zero.

 

[PG1995]

Hi

Could you please help me with this query? Thank you.

Regards
PG

 

[steveB]

You have to be very careful when you use the atan function because it does not always give you the correct quadrant. If you look at the answer in rectangular coordinates, you'll see that the vector is pointing in the correct direction (147.4 degrees, which is 180 degrees opposite -32.6 degrees). If you use atan, then you need to identify the quadrant of the unit circle, in order to get the correct angle. Alternatively, you can use the atan2 function which is available in Matlab.

 

[PG1995]

Thank you.

But I can't have access to Matlab all the time. I have checked the manuals of the Casio calculator and TI-89, they don't list any extra atan function. I'm just curious to know how to handle this without Matlab. Could you please let me know if there is a way? Thanks a lot.

PS: I understand it now. Here is how to do this. In that example y > x and x < 0 so I need to add 180° to -32.6 to get correct angle.

Best wishes
PG

Reference:
1: https://en.wikipedia.org/wiki/Atan2