Why is current amplitude not expressed as a function of time?

[kent davidge]

I found this answer for an question of the Halliday's book but the units m².T.rad/s in the answer don't make sense with voltage. (sorry my poor english)
And I cannt understand why they haven't expressed the current as a function of time.

 

[Vagn]

I found this answer for an question of the Halliday's book but the units m².rad/s in the answer don't make sense with voltage. (sorry my poor english)
And I cannt understand why they haven't expressed the current as a function of time.

You have missed the T (tesla) in the permeability of free space.

 

[kent davidge]

You have missed the T (tesla) in the permeability of free space.

Okay, I notice that. Can you explain me why the current was not expressed as a function of time? I learned from the Faraday's formula that the flux's variation is basically a derivative which involves the time.

 

[nasu]

Because what they wrote is the amplitude of the emf.
The amplitude is not time dependent. The formula includes the amplitude of the current, io.