The resistance of the loop in FIGURE EX30.15 is $0.20\mathrm{\Omega }$Is the magnetic field strength increasing or decreasing? At what rate T/s ?

The result called as the Faraday-Lenz law. In practice, we often pander magnetic induction in multiple wire coils, each of which contributes the same EMF. As a result, an extra term representing the amount of turns, i.e. What is the connection between Faraday's law of induction and also the magnetic force

The induced current, because of Lenz's law, is such it produces its own field that opposes the change in magnetic flux of external field. Using the proper hand rule, we discover that sector because of the induced current within the loop points out of the paper. Therefore, the direction of change of external magnetic field points inside the paper. Since the sphere is already directed into the paper, this alteration increases the strength of the sector. To find the rate at which this increase happens we use the Faraday's law of electromagnetic induction which says that the induces emf within the circuit is up to

$\epsilon =\left|\frac{\mathrm{\Delta \Phi }}{\mathrm{\Delta }t}\right|=A\left|\frac{\mathrm{\Delta }B}{\mathrm{\Delta }t}\right|=a^2\left|\frac{\mathrm{\Delta }B}{\mathrm{\Delta }t}\right|$

where $a=8.0\mathrm{cm}$. Now, from Ohm's law

$I=\frac{\epsilon }{R}=\frac{a^2}{R}\left|\frac{\mathrm{\Delta }B}{\mathrm{\Delta }t}\right|$

From this equation we duscover

$\left|\frac{\mathrm{\Delta }B}{\mathrm{\Delta }t}\right|=\frac{IR}{a^2}=4.7\frac{\mathrm{T}}{\mathrm{s}}.$

The field strength increases at the speed of $4.7\mathrm{T}/\mathrm{s}$