Video Transcript
Quantity 𝑎 has dimensions of 𝐼 times 𝑇 squared. Quantity 𝑏 has dimensions 𝑇 to the negative two times 𝑀 to the negative one. What are the dimensions of 𝑎 times 𝑏?
We can symbolize the dimensions of 𝑎 like this. They are 𝐼, that’s current, times 𝑇, that’s time, squared. Similarly, the dimensions of 𝑏 are 𝑇, time, to the negative two times 𝑀, mass, to the negative one. We want to solve here for the dimensions of 𝑎 times 𝑏. This is equal to the dimensions of 𝑎 times the dimensions of 𝑏. That’s equal to current times time squared multiplied by time to the negative two times mass to the negative one. When we multiply 𝑇 squared by 𝑇 to the negative two, the result of that is one, leaving us with dimensions of current 𝐼 times mass 𝑀 to the negative one. The dimensions of 𝑎 times 𝑏 equal 𝐼 times 𝑀 to the negative one.
