A uniform magnetic field ¯B=(3^i+4^j+^k) exists in region of space. A semicircular wire of radius 1 m carrying current 1A having its centre at (2, 2, 0) is placed in x-y plane as shown in figure. The force on semicircular wire will be
√2(^i−^j+^k)
Force on semicircular wire = force on section PQ.
∴→F=i(→l×→B)
Here →l=−−→PQ=(2 cos 45∘)^i+(2 sin 45∘)^j
=(√2^i+√2^j)m∴→F=(1)[(√2i+√2j)]×(3^i+4^j+^k)=√2(^i−^j+^k)