The direction of the force exerted on a current-carrying conductor perpendicular to a magnetic field can be visualized by means of the left-hand rule illustrated in Figure 1.  (There are several hand rules for this purpose.  The following is only one suggestion.)

 

Figure 1

Hold your left hand flat with outstretched fingers in the direction of the magnetic field ( B→ ) and with the thumb pointing off to one side in the direction of the negative current flow. The palm of your hand will then be pointing in the direction of the magnetic force ( F→ ) that acts on the conductor.


           

Read Unit Introduction
Read "Left-hand Rule for Magnetic Force" on page 604 of the textbook for a summary.  To further your understanding, view the animation Left-hand Rule of Magnetic Field.


Magnetic Force Magnitude

By combining the equation that describes the magnetic force acting on a moving, charged particle with the definition of electric current, it is possible to determine the size of the magnetic force acting on a current-carrying conductor (assuming the current direction is perpendicular to the magnetic field).

magnetic force on a charged particle

 

current


Combining both equations and treating the velocity in terms of units gives an equation that describes the size of the magnetic force acting on a current ( I ) carrying conductor of specific length ( l ), which is perpendicular to a magnetic field ( B ).


 

Expressed as an equation, .



Magnetic Force:  The deflecting magnetic force acting on a current-carrying conductor is proportional to the product of the conductor's length in the field and the current it carries perpendicular to the magnetic field at its location.

Expressed as an equation


Fm=IlB  if I ⊥B→


 

Quantity

Symbol

SI Unit

magnetic force

F

newton (N)

current

I

ampere (A)

length of conductor

l

metres (m)

strength of the magnetic field

B

tesla (T)

 

In cases where only a component of the current and/or magnetic field are perpendicular, only the components that are perpendicular are used to calculate the size of the magnetic force.


 

Example Problem 1.

 

Determine the magnitude and direction of the magnetic force acting on a 0.500 m long conductor that carries a 2.00 A e - flow current west through a 3.50 × 10 -1 T magnetic field that is directed north.

 

Given

 

 

Magnitude

 

F m = IlB
F m = (2.00 A)(0.500 m)(3.50 × 10 -1 T)
F m = 3.50 × 10 -1 N

 

Direction

 

 

According to the left-hand rule for negative charges, the force is upward.

 

Paraphrase

 

The magnetic force acting on the wire is 3.50 × 10 -1 N [up].