23dF= i ( dL x B)
i think u missed out that F is a vector product of idL and B
A simple hcv sum with so much vectors is eating my head.... the concept is right but maths
Consider a hypothethical magnetic field in a region B=B0er where er is the radial vector. A circlular loop of raidus a carrying a current i is placed with its palne parallel to X-Y plane and its centre at (0,0,d) Find the magnitude of magnetic force acting on it.
The first thing i noticed was that if it is a circle then x2+y2+z2=a2+d2 so then
i used then i used the formula by ilb by replacing l by dl.......
its componets will be dL x/√a^2+d^2 means using the concept that component is Ax/A where A is the total magnitude but i am unable to get the answer...... any comments
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3 Answers
231no man i am an expert in making silly mistakes but not such a champion could u pls post the solution
106er = cosθz + sinθcosφx + sinθsinφy,
θ is angle from z axis and φ is angle from x-axis
and dl = (-sinφx + cosφy)*(adφ)
dl x B = (sinφcosθy - sinθsin2φz +cosθcosφx - sinθcos2φz)*(Ba dφ)
if you integrate wrt φ from 0 to 2π then the terms involving sinφ and cosφ will be zero
only thing left is Ba z ∫02π(-sinθ)dφ
= -2πBasinθ z
to calculate sinθ = d(a2+d2)0.5
NOTE : i have used spherical coordinates. you can look them up in wiki
otherwise you will have to use symmetry to argue that x and y components of the force will be zero as it is symmetric. and then calculate only the z component of the force.