Magnetic Force on a Current-Carrying Wire — Question 2

Question 2

A horizontal wire can balance its weight with a transverse magnetic force

A straight horizontal wire has length L=.400 m and mass m=.0200 kg. A uniform .250 T field points into the page. The current flows to the right. Ignore forces on the remote return path and use g=9.81 m/s squared.

1. Find the current required for the magnetic force to balance the wire weight.

2. If the current is reversed at the same magnitude, find the upward support force needed to hold the wire stationary.

Question 2 - Solution

A horizontal wire can balance its weight with a transverse magnetic force

(a) Method and calculation

$$\vec F_B=ILB\hat y,\quad ILB=mg.$$$$I=\frac{mg}{LB}=\frac{(.0200)(9.81)}{(.400)(.250)}=1.962\,\mathrm A.$$

(b) Interpretation and further calculation

$$I\to-I:\quad\vec F_B=-mg\hat y.$$$$F_{\mathrm{support}}-mg-mg=0\Rightarrow F_{\mathrm{support}}=2mg=.3924\,\mathrm N.$$

Physical check

Reversing current reverses the magnetic force; gravity is unchanged.