Question

A magnetic field in a region of space produced by a long straight wire carrying a current I has the form 𝑩 = 𝜇0𝐼 2𝜋𝑟 𝝋̂ , where r is the perpendicular distance from the z-axis and 𝝋 is a unit vector in the circumferential direction. A test wire is positioned in the magnetic field at a distance r and carries a current flowing in the positive z-direction. If the test wire has length L, calculate the force on the wire using the Lorentz force formula.

Answer 1

As per the given question,

Magnetic field in the region $(B)=\frac{\mu_o I}{2\pi r}\hat{\varphi}$

Length of the test wire is L and the current in the wire is L

Hence Lorentz force on the test wire is $(F)=iB\times L$

Hence, $F=\frac{\mu_o I^2L}{2\pi r}\hat{\varphi}$