Physics Lesson 16.3.2 - The Direction of Magnetic Force. Fleming's Left Hand Rule

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Welcome to our Physics lesson on The Direction of Magnetic Force. Fleming's Left Hand Rule, this is the second lesson of our suite of physics lessons covering the topic of Magnetic Force on a Current Carrying Wire. Ampere's Force, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

The Direction of Magnetic Force. Fleming's Left Hand Rule

The direction of magnetic force calculated through the formula of Ampere's Force is found by using the so-called "Fleming's Left Hand Rule". It consists of three steps:

The left hand is completely open; the thumb forms an angle of 90° to the other four fingers.
The four fingers show the current direction.
The magnetic field lines punch the open palm.

If these three rules are applied properly, then the thumb shows the direction of magnetic force, as shown in the figure.

Physics Tutorials: This image provides visual information for the physics tutorial Magnetic Force on a Current Carrying Wire. Ampere's Force

There are two other versions of left hand rule application as well. One is the three fingers version (FBI) where the thumb shows the force, the index finger the direction of magnetic field and the middle finger the current, as shown in the figure below.

The other version is the following one:

Henceforth we will use the first version of Fleming's LHR in all situations to avoid confusion.

Example 1

The electric circuit shown in the figure below produces a 3A current when the switch is closed. The circuit is placed normal to a uniform magnetic field of induction equal to 5 mT. A 20 cm metal bar is placed perpendicular with the two horizontal circuit sides. The switch is initially open. Then, it turns ON for a very short time and is switched off again.

What is the moving direction of the metal bar immediately after the switch is open?
What is the magnitude of magnetic force produced on the bar? Suppose almost all the current flows only through the bar when the circuit is open.
What is the mass of the bar if it starts accelerating from rest at 0.2 m/s2 when the switch turns on?

Solution 1

The cross symbols mean the magnetic field lines enter the page normal to it. Thus, the palm must be directed out of page.
Electric current flows in the anticlockwise direction when the switch is open. This means the current in the bar flows in the down-up direction, so the four fingers will be directed upwards.
From here, we can find the direction of the magnetic force applying the Fleming's Left Hand Rule. Putting the hand in the required direction, we find that the magnetic force shown by the thumb acts due left.
Clues:
I = 3A
B = 5 mT = 0.005 T
L = 20 cm = 0.20 m
F = ?
From the formula derived from the Fleming's Left Hand Rule (the scalar version), we obtain
F = I ∙ L ∙ B ∙ sin⁡θ
where sin θ = 1 because all components of the formula are perpendicular to each other (sin 90° = 1). Thus, substituting the values, we obtain
F = (3A) ∙ (0.20m) ∙ (0.005T) ∙ 1
= 0.003 N
From the Newton's Second Law of Motion, we have
a = F/m
where m is the mass of the conducting rod, F is the magnetic force acting on the rod and a is its acceleration. Therefore, rearranging the above formula we obtain for the mass m of the rod:
m = F/a
= 0.003 N/0.2 m/s²
= 0.015 kg
= 15 g

The same procedure is also used when the angle between the current and magnetic field lines is not 9°. Let's consider an example.

Example 2

A current carrying bar is used to connect two detached parts of an electric circuit as shown in the figure.

What are the horizontal and vertical components of magnetic force acting on the bar if the value of magnetic induction is 20 mT?

Solution 2

The direction of magnetic field is out of the page, normal to its plane. In addition, the value of electric current flowing through the circuit (and therefore through the metal bar) is calculated applying the Ohm's Law where ε = 12 V and R = 30 Ω. Therefore, we obtain for current:

I = ε/R
= 12 V/30 Ω
= 0.4 A

The direction of magnetic field is still perpendicular to the current, regardless the angle shown in the figure. This is because the electric current lies according the plane of the figure while magnetic field is normal to it. Therefore, we have for the magnitude of magnetic force produced:

F = I ∙ L ∙ B ∙ sinθ

where sin θ = 1 because L and B of are perpendicular to each other (sin 90° = 1). Thus, giving that L = 10 cm = 0.10 m and B = 20 mT = 0.020 T, we obtain after substitutions

F = (0.4 A) ∙ (0.10 m) ∙ (0.020 T) ∙ 1
= 0.0008 N

Using the Fleming's left hand rule (the palm is directed onto the page, the four fingers are in the up-right direction) the magnetic force shown by the thumb is directed inwards the circuit perpendicular to the bar. The horizontal component F_x of the magnetic force is

F_x = F ∙ cos⁡(90⁰ - 53⁰ )
= 0.0008 N ∙ cos⁡37⁰
= 0.0008 N ∙ 0.8
= 0.00064 N (due right)

and the vertical component F_y of the magnetic force is

F_y = F ∙ sin⁡(90⁰ - 53⁰ )
= 0.0008 N ∙ sin⁡37⁰
= 0.0008 N ∙ 0.6
= 0.00048 N (down)

The figure below shows these magnetic force components.

You have reached the end of Physics lesson 16.3.2 The Direction of Magnetic Force. Fleming's Left Hand Rule. There are 5 lessons in this physics tutorial covering Magnetic Force on a Current Carrying Wire. Ampere's Force, you can access all the lessons from this tutorial below.

More Magnetic Force on a Current Carrying Wire. Ampere's Force Lessons and Learning Resources

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Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.3	Magnetic Force on a Current Carrying Wire. Ampere's Force
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.3.1	Magnetic Force on a Current Carrying Wire. Ampere's Force
16.3.2	The Direction of Magnetic Force. Fleming's Left Hand Rule
16.3.3	Magnetic Force between two Parallel Current Carrying Conducting Wires
16.3.4	Magnetic Force on a Current Carrying Loop. The Motor Effect
16.3.5	Electric Motor

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Physics Lesson 16.3.2 - The Direction of Magnetic Force. Fleming's Left Hand Rule

The Direction of Magnetic Force. Fleming's Left Hand Rule

Example 1

Solution 1

Example 2

Solution 2

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