Question

please make the solution and the picture clear

3. 6A current-carrying wire is bent into a closed semicircular loop of radius R that lies in the x, y plane (Figure below). The wire is in a uniform magnetic field that is in the +z direction, as shown. Verify that the force acting on the loop is zero. (problem 26.25). [20 marks]

Answer 1

аF аe Rd6 de о х

the magnetic force due to the external magnetic field and the current flowing in the loop is in the radial
direction

integrate the element
of force dF acting on an element of length
dℓ between θ = 0 and π to find the force
acting on the semicircular portion of the
loop

F = Fsemicircular loop + Fstraight segment

Fstraight segment
= I lXB = -2RIB

force dF acting on the
element of the wire of length dℓ:
dF = IdlB = IRBdθ

dFx= dF cosθ
and
dFy= dF sinθ
by symmetry, the x

integral of dFy
= integral of IRBsinθ dθ

Fy = RIB integral of sinθ dθ
0 to pi
Fy = 2RIB

Net force = -2RIB + 2RIB = 0