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My teacher said
e^{2} 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 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.
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.
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.
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.
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.
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.