Question

The plane of a loop of wire is perpendicular to a magnetic field. Rank, from greatest to least, the magnitudes of the loop's induced emf for each situation. A. The magnetic field strength increases from 0 T to 1 T in 6 s. B. The magnetic field strength increases from 1 T to 4 T in 2 s. C. The magnetic field strength remains at 4 T for 1 min. D. The magnetic field strength decreases from 4 T to 3 T in 4 s. E. The magnetic field strength decreases from 3 T to 0 T in 1 s.

Answer 1

Answer:

E - B - D - A - C

Explanation:

The magnitude of the emf induced in the loop of wire is given by Faraday-Newmann-Lenz

$\epsilon=\frac{\Delta \Phi_B}{\Delta t}$ (1)

where

$\Delta \Phi_B$ is the variation of magnetic flux

$\Delta t$ is the time interval

Rewriting the flux as product between magnetic field strength (B) and area enclosed by the coil (A):

$\Phi_B = BA$

and since the area of the coil does not change, the variation of flux can be rewritten as

$\Delta \Phi_B = \Delta B A$

So (1) becomes

$\epsilon=\frac{\Delta B}{\Delta t}A$

Which means that the induced emf is proportional to the rate of change of the magnetic field, $\frac{\Delta B}{\Delta t}$. So we just need to calculate this quantity for each scenario, and rank them from greatest to latest.

We have:

A) $\frac{\Delta B}{\Delta t}=\frac{1 T - 0T}{6 s}=0.167 T/s$

B) $\frac{\Delta B}{\Delta t}=\frac{4 T - 1T}{2 s}=1.500 T/s$

C) $\frac{\Delta B}{\Delta t}=\frac{4 T - 4T}{60 s}=0 T/s$

D) $\frac{\Delta B}{\Delta t}=\frac{3 T - 4T}{4 s}=-0.250 T/s$

E) $\frac{\Delta B}{\Delta t}=\frac{0 T - 3T}{1 s}=-3.000 T/s$

So, from greatest to least magnitude, we have:

E - B - D - A - C

Answer 2

The plane of a loop of wire is perpendicular to a magnetic field. Rank, from greatest to least, the magnitudes of the loop's induced emf for each situation will be E - B - D - A-C.

What is magnetic field strength?

The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.

The magnitude of the  induced emf in the loop of wire is;

$\rm \epsilon = \frac{\triangle \phi }{ \triangle t}$

The megnetic flux is given by;

$\phi_B= \triangle BA$

$\rm \epsilon = \frac{ \triangle BA }{ \triangle t}$

The above expression shows that the induced emf is proportional to the rate of change of the magnetic field,

$\rm \frac{ \triangle B }{ \triangle t} = \frac{ 1T-0T }{ 6} =0.167\ T/sec$

$\rm \frac{ \triangle B }{ \triangle t} = \frac{ 4T-1T }{ 2} =1.500\ T/sec$

$\rm \frac{ \triangle B }{ \triangle t} = \frac{ 4T-4T }{ 60} =0\ T/sec$

$\rm \frac{ \triangle B }{ \triangle t} = \frac{ 3T-4T }{ 4} =-0.25 \ T/sec$

$\rm \frac{ \triangle B }{ \triangle t} = \frac{ 0T-3T }{ 1} =-3 \ T/sec$

From the above, it is observed that Rank, from greatest to least, the magnitudes of the loop's induced emf for each situation will be E - B - D - A-C.

Hence the order will be E - B - D - A-C.

To learn more about the strength of induced magnetic field refer to;

https://brainly.com/question/2248956