Find magnetic force on a squar loop

[leonne]

Homework Statement

suppose that mag field is B=kz $$\stackrel{^}{x}$$
find force on a square loop(side a) lying in the yz plane and centers at origin, if it carries a current I flowing counter clock whne u look down x axis

Homework Equations

Fmag=I$$\int$$(dl x B)

The Attempt at a Solution

Why does The force on the left side (toward
the left) cancels the force on the right side (toward the right)? Also than the answer is
netforce= 2(IaB)=2(Ia(ka/2)=Ia²k up

How did B turn into ka/2? and where did the "a" come from?

 

[tiny-tim]

hi leonne!

(have an integral: ∫ and try using the X² icon just above the Reply box )

suppose that mag field is B=kz $$\stackrel{^}{x}$$
find force on a square loop(side a) lying in the yz plane and centers at origin, if it carries a current I flowing counter clock whne u look down x axis

Homework Equations

Fmag=I$$\int$$(dl x B)

…the answer is
netforce= 2(IaB)=2(Ia(ka/2)=Ia²k up

How did B turn into ka/2? and where did the "a" come from?

(do you mean B = kz^x ? )

B is kz along the lines z = ±a/2, so B = ±ka/2

 

[leonne]

hmm tried to make it B=kz x^ (x hat)
o ok thxs hmm