Physics: Relationship between Right Hand Rule and Cross Product

The right-hand rule is used by Physicists to remember the direction of magnetic forces in a magnetic field. It is in fact a hand mnemonic used in Physics and Mathematics.

Physics: Relationship between Right Hand Rule and Cross Product

The right hand rule is used by Physicists to remember the direction of magnetic forces in a magnetic field. It is in fact a hand mnemonic used in Physics and Mathematics.

Students often get confused while interpreting the right-hand rule or even when applying the rule practically. This rule is mostly used in Physics but also has some applications in Mathematics.

We will explain the right-hand rule in detail with images so that you can confidently solve your academic assignments with a bang. We will also explain the relationship between the right-hand rule and cross-product in terms of Physics.

What is Right-Hand Rule?

Right-Hand Rule can be defined as,

In physics and mathematics, the right hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space.

The fact that the three axes of three-dimensional space have two alternative orientations gives rise to the majority of the several right-hand and left-hand laws.

Keeping one's hands outward and together, palms out, and thumb outstretched will make it observable.

If the curl of the fingers represents a movement from the first or x-axis, to the second or y-axis, the third, or z-axis, will point along with either thumb.

Coordinates are normally right-handed. The right thumb points to the Z-axis in the positive direction for right-handed coordinates.

 However, the curl of the fingers reflects a rotation from the first or X-axis to the second or Y-axis. The mechanism rotates counter-clockwise as seen from the top or Z axis.

How is Cross Product and Right-Hand Rule related?

Cross product is often used in Physics to multiply two vectors. It is a very important concept in Physics. However, vector product has one limitation. One cannot tell the direction of the cross product when multiplying two vectors.

This is where the right-hand rule comes into play. The direction of the cross product can be evaluated by implementing the right-hand rule. In fact, the cross product of two vectors is represented by using the right-hand rule. To apply the right-hand rule to cross the product of two vectors, follow these steps.

  1. The index finger points in the direction of the velocity vector v.
  2. The middle finger points in the direction of the magnetic field vector B.
  3. The thumb points in the direction of the cross-product F.

To find a cross product of two vectors, you can use an online cross product calculator. If you need to find a dot product, you can also use any dot product calculator online.

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Applications of Right Hand Rule

  1. A straight wire conducts an electric current. As the thumb points in the direction of the traditional current, the twisted fingers point in the direction of the magnetic flux lines around the conductor. The magnetic field's orientation would be counterclockwise as an outcome of this convention, not an intrinsic physical phenomenon.
  2. A magnetic field is generated when an electric current flows through a solenoid. When the right hand is wrapped around the solenoid with the fingers pointing in the direction of the conventional current, the thumb points in the direction of the magnetic north pole.
  3. The right-hand rule can be used to find the direction of electromagnetic fields, enantiomers, rotation, mirror images, spirals, and magnetic fields.

 

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