Which of the following is a scalar quantity?

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3 years ago

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A -turn rectangular coil with length and width is in a region with its axis initially aligned to a horizontally directed uniform

madam [21]

Complete Question

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Answer:

The maximum emf is $\epsilon_{max}= 26.8 V$

The emf induced at t = 1.00 s is $\epsilon = 24.1V$

The maximum rate of change of magnetic flux is $\frac{d \o}{dt}|_{max} =26.8V$

Explanation:

From the question we are told that

The number of turns is N = 44 turns

The length of the coil is $l = 15.0 cm = \frac{15}{100} = 0.15m$

The width of the coil is $w = 8.50 cm =\frac{8.50}{100} =0.085 m$

The magnetic field is $B = 745 \ mT$

The angular speed is $w = 64.0 rad/s$

Generally the induced emf is mathematically represented as

$\epsilon = \epsilon_{max} sin (wt)$

Where $\epsilon_{max}$ is the maximum induced emf and this is mathematically represented as

$\epsilon_{max} = N\ B\ A\ w$

Where $\o$ is the magnetic flux

N is the number of turns

A is the area of the coil which is mathematically evaluated as

$A = l *w$

Substituting values

$A = 0.15 * 0.085$

$= 0.01275m^2$

substituting values into the equation for maximum induced emf

$\epsilon_{max} = 44* 745 *10^{-3} * 0.01275 * 64.0$

$\epsilon_{max}= 26.8 V$

given that the time t = 1.0sec

substituting values into the equation for induced emf $\epsilon = \epsilon_{max} sin (wt)$

$\epsilon = 26.8 sin (64 * 1)$

$\epsilon = 24.1V$

The maximum induced emf can also be represented mathematically as

$\epsilon_{max} = \frac{d \o}{dt}|_{max}$

Where $\o$ is the magnetic flux and $\frac{d \o}{dt}|_{max}$ is the maximum rate at which magnetic flux changes the value of the maximum rate of change of magnetic flux is

$\frac{d \o}{dt}|_{max} =26.8V$

8 0

2 years ago