A flexible conducting wire is bent to form a semicircle of radius and carries a…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A flexible conducting wire is bent to form a semicircle of radius R and carries a steady current I directed anticlockwise when viewed from above. The plane of the semicircle lies in a uniform magnetic field of magnitude B directed vertically upward.
(i) Consider a small element of the wire subtending an angle dθ at the centre. Write an expression for the differential magnetic force on this element in vector form.
(ii) Integrate over the entire semicircle to obtain the magnitude of the net magnetic force on the wire. Express your result in terms of I, B, and R.
(iii) State the direction of the net force and comment on how it depends on the radius of the semicircle.