A semi circular current carrying wire having radius R is placed in x-y plane with its centre at origin ‘O’. There is non-uniform magnetic field B⃗ = B𝑜x 2𝑅k̂ (here Bo is +ve constant) is existing in the region. The magnetic force acting on semi circular wire will be along :-

Question

G1 Physics · Accepted Answer

For an element dF⃗=I dℓ⃗×B⃗ and the z-component of field is B₀x/(2R). Parameterize the semicircle by x=Rcosφ and integrate over φ. The y-components cancel and the remaining force is along -x. Hence A.