Verification of my solution to a problem of Magnetism

[Swapnil Das]

 

[TSny]

Your equation for $\vec{dF} = I \vec{dI} \vec{B}$ doesn't make sense as written. How do you interpret $\vec{dI} \vec{B}$? Is this a product of two vectors? If so, what type of product?

Later you write $dT = I \vec{B} \; \vec{dl}$. Again the right hand side doesn't indicate the type of product of the two vectors. Also, the left hand side $dT$ is written as a scalar rather than a vector. It appears that you are assuming that the tension in a segment $dl$ is equal to the magnetic force on the segment. Is that correct? You need to draw a free body diagram for the segment $dl$.

 

[Swapnil Das]

Your equation for $\vec{dF} = I \vec{dI} \vec{B}$ doesn't make sense as written. How do you interpret $\vec{dI} \vec{B}$? Is this a product of two vectors? If so, what type of product?

Later you write $dT = I \vec{B} \; \vec{dl}$. Again the right hand side doesn't indicate the type of product of the two vectors. Also, the left hand side $dT$ is written as a scalar rather than a vector. It appears that you are assuming that the tension in a segment $dl$ is equal to the magnetic force on the segment. Is that correct? You need to draw a free body diagram for the segment $dl$.

Thanks a lot, Sir!