Question

A -turn rectangular coil with length and width is in a region with its axis initially aligned to a horizontally directed uniform magnetic field of mT and set to rotate about a vertical axis with an angular speed of rad/s. What is the maximum induced emf in the rotating coil? What is the induced emf in the rotating coil at ? What is the maximum rate of change of the magnetic flux through the rotating coil?

Answer 1

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
`(d \o)/(dt)|_(max) =26.8V`

Step-by-step 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 = (15)/(100) = 0.15m`

The width of the coil is
`w = 8.50 cm =(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) = (d \o)/(dt)|_(max)`

Where
`\o` is the magnetic flux and
`(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

`(d \o)/(dt)|_(max) =26.8V`