# Very Very simple question on dimensions of equation

In summary, My teacher explained the dimensions of c ħ/R as (distance/time)*(energy*time)/(distance), which can also be written as L-1MT and MT^2. To calculate something like LMT/M^2, it is best to put the units into the expression and treat them as algebraic variables.

My teacher said

e2 c x ħ/R

Where e is the electric charge, c is speed of light and h is reduced constant and R is radius.

My teacher said this has dimenions of energy, is this right?

c ħ/R has dimensions of (distance/time)*(energy*time)/(distance), or energy.

Multiplying by the square of the electrical charge yields (charge)2*(energy), which does not have dimensions of energy.

D H said:
c ħ/R has dimensions of (distance/time)*(energy*time)/(distance), or energy.

Multiplying by the square of the electrical charge yields (charge)2*(energy), which does not have dimensions of energy.

Ok thank you. I have another question. My teacher was showing us a way to check the dimensions of equations. He showed us this

LMT

So if something has mass x t dimensions, it can be given as

LMT/L

it can also be written as L-1MT is this right?

If I wanted to multiply two values together, let us say MT times T this is just

MT2

right?

How do you calculate something like

LMT/M2

Thanks

What the teacher is telling you is fine so long as you don't mix up, say, seconds and hours or meters and centimeters, etc.

MT times T is MT^2

LMT/M^2 = L(M^-1) T

In my opinion the better way to do it is put the units into the expression and handle them just like the units are typical algebraic variables and see if the units remaining in the expression are what you seek.

Yes, your teacher is correct. The dimensions of the given equation are of energy. This can be seen by breaking down the equation into its constituent parts and analyzing their dimensions.

The first term, e, represents the electric charge, which has dimensions of charge (Q). The second term, c, represents the speed of light, which has dimensions of distance divided by time (LT^-1). The third term, ħ, represents the reduced Planck constant, which has dimensions of energy multiplied by time (ET). The fourth term, R, represents radius, which has dimensions of distance (L).

When we substitute these dimensions into the equation, we get:

(Q)(LT^-1)(ET)(L^-1)

Simplifying, we get:

QELT^-2

This is the dimension of energy, as Q represents charge, E represents energy, and T^-2 represents the inverse of time squared. Therefore, your teacher is correct in stating that the given equation has dimensions of energy.

## 1. What are dimensions in an equation?

Dimensions in an equation refer to the units of measurement used for each variable in the equation. They are important because they ensure that the equation is balanced and makes sense in the context of the problem being solved.

## 2. How do you determine the dimensions of an equation?

The dimensions of an equation can be determined by looking at the units of measurement for each variable and using dimensional analysis to ensure that the units on each side of the equation are equivalent. This involves converting all units to their base units and cancelling out any common units on both sides of the equation.

## 3. Why is it important to include dimensions in an equation?

Including dimensions in an equation is important because it helps to ensure that the equation is accurate and meaningful. It also allows for easier conversion between units and helps to identify any errors in the equation.

## 4. Can an equation have different dimensions on each side?

No, an equation must have the same dimensions on both sides to be considered balanced. This is because the units of measurement must cancel out to give a dimensionless quantity, or else the equation would not make sense.

## 5. Can dimensions be manipulated in an equation?

Yes, dimensions can be manipulated in an equation as long as the units of measurement are equivalent on both sides. This is known as dimensional analysis and is often used to convert units or solve for unknown variables in an equation.