Very Very simple question on dimensions of equation

[HelpNowPlease]

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?

 

[D H]

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.

 

[HelpNowPlease]

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

 

[LawrenceC]

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.

 

[asteriatic]

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.