Example: Magnetic Field

Problem

A Metal Rod with length 1.2 m and mass 500 g is suspended in a magnetic field of 0.9 T. Determine the current needed suspend the rod without supports.

Figure will be shown here

Solution

Ampere's Force Law

$\overrightarrow{F}=\underset{c}{\int }I\overrightarrow{d}l\times \overrightarrow{B}$

For our problem we have $\overrightarrow{B}=0.9T$

And we know the necessary Force to hold up the bar without the supports would be equal to the weight of the bar multiplied by the gravitational force.

${\overrightarrow{F}}_{\text{needed}}=\text{mass}\times \text{gravity}$

$\overrightarrow{F}=500*9.81(g*m/s^2)$

$\overrightarrow{F}=4.905(N)$

Substituting into Ampere's Law we are left with

$4.905=\underset{c}{\int }I\overrightarrow{d}l\times 0.9(T/N)$

Integrating from l=0 to l=1.2 m gives us

$4.905=I*1.2*0.9(T*m/N)\to I=4.905/(1.2*0.9)=4.5417A$

In conclusion we would need 4.54 Amps of current to suspend the bar in the magnetic field.