One ring to bring them all and in the darkness bind them.
If a ring can do that, why a hand can't?
Of course, it can!
In physics, different books are full of a lot of hand rules which I personally find rather confusing and difficult to remember. Some of them are:
1) Fleming's Left Hand Rule - If a current carrying wire is placed in an external magnetic field, the wire experiences a force perpendicular both to the field and to the direction of current. The direction of force can be given by Fleming's left hand as illustrated below:
Fleming's Left Hand Rule
2) Fleming's Right Hand Rule - If a wire is moving in an external magnetic field, there is a current induced in the wire, direction of which can be given by Fleming's right hand rule as illustrated below:
Fleming's Right Hand Rule
These are two rules specific to two cases. Although they can be applied to few other scenarios as well, it's always confusing which hand to use in which situation. To get rid of this, I'll be explaining a simple method "Right Hand Rule" where you don't need to remember such complicated convention. In this method, you need to keep only one thing in mind - "Always use a right hand! If you don't have a right hand, borrow from someone else but always use a right hand only!"
Let's start with vector cross products. Example `\vec\tau = \vecR X \vecF`
Let's use our right hand to determine the direction of Torque when direction of Force and Radius vector are known.
Step 1) Note down the first element of the cross product. Here it's `\vecR`. Place the fingers of your right hand along this vector such that your little finger lies on the first vector.
Step 2) Now, try to curl the fingers towards the second vector i.e. `\vecF`. Keep in mind that you are not defying the laws of nature while doing so. Your fingers should always curl towards a closed palm and not in the reverse direction. If other vector is on the back side of your palm, flip your hand and place the fingers on `\vecR` in such a manner that your index finger lies on it. Now you should be able to close the fingers without breaking them.
Step 3) Note down the angle your fingers moved. Ideally it should be between 0 and 180 degrees if you followed the steps correctly. Even if you get something larger than 180 degrees, the expression will take care of it so you don't need to worry.
Step 4) Once you are done curling your fingers, your thumb is pointing in the direction of the torque and it's magnitude is given by `\tau = RF\sin\theta` where `\theta` is the angle you got in step 3. If you got an angle larger than 180 degrees, this expression will be negative and thus the direction of torque will be in direction opposite to your thumb. Simple as that!
Now, let's see if we can follow the same procedure and get the results of Fleming's left hand rule:
Motion will be in the direction of force and the force is given by: `\vecF = I\vecLX\vecB` which is essentially a vector cross product.
Keep your hand in the direction of current (because that is the direction of `\vecL`) i.e. along the middle finger of the first figure. Now curl the fingers towards the magnetic field which points along the index finger of the first figure. You will find that your thumb is pointing in the same direction as given by Fleming's left hand rule.
For the Fleming's right hand rule, we need to find the direction of current. To do this, let's find out where a positive charge placed inside the conductor would go (because that's the direction of the current). The positive charge will move in the direction of magnetic force which is given by: `\vecF = q\vecv X \vecB`. Velocity of the positive charge `\vecv` points in the direction of motion i.e. thumb in the second figure. Magnetic field points in the direction of index finger and thus when you curl your fingers, your thumb will be pointing in the direction of middle finger i.e. the current. Try it yourself.
Same concept can be used to tell the direction of magnetic field produced by a straight wire as well as a curved wire. Magnetic field due to a small element of wire (which is essentially straight) is given by:
`\vecB = (i\vec(dL) X \vecr)/r^3`
This expression along with the concepts learnt above can determine the direction of magnetic field. However, direction of field can be easily decided as per the following method:
1) For a straight current carrying conductor, place your thumb along the wire in the direction of current. Your fingers will curl around the wire and will give the direction of magnetic field.
2) For a curved current carrying conductor such as a loop, place your fingers along the current (because you simply can't place a thumb along a curved line). your thumb will point in the direction of magnetic field.
Try it out a few times and you will never get it wrong. This process is so simple that you will have to try hard to get it wrong.
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