The magnetic flux through a metal ring varies with time t according to φb = at3 − bt2, where φb is in webers, a = 6.00 wb s−3, b = 18.0 wb s−2, and t is in seconds. the resistance of the ring is 2.80 ω. for the interval from t = 0 to t = 2.00 s, determine the maximum current induced in the ring.

To solve this problem it is necessary to apply the second derivative of the function to find the maximum time reference and thus calculate the maximum voltage.

With the maximum voltage by Ohm's Law it is possible to find the maximum current.

Ohm's law defines that

E = I*R

Where,

I = Current

R= Resistance

On the other hand by faraday studies and the potential can be expressed at the rate of change of the electric flow, that is

Replacing with our values we have that

The second derivative is

When E' = 0 we have a Maximum, then

0 = -36t+36

t = 1

Therefore when the time is 1s E has a Maximum, replacing at the function

Then the maximum current will be given by

Therefore the maximum current induced in the ring is 6.42A

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

i believe the answer is a hope it and is correct