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

${\vec {F}}=\int \limits _{c}I~{\vec {d}}l\times {\vec {B}}$

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

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.

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

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

${\vec {F}}=4.905~~(N)$

Substituting into Ampere's Law we are left with

$4.905=\int \limits _{c}I~{\vec {d}}l\times 0.9~~(T/N)$

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

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

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