###### Permanent Magnet and Electromechanical Devices

73 SOLVED PROBLEMS

Question: C.3.1

## Apply the fourth-order Runge-Kutta method to the equations for rotational motion (5.87). ...

The equations governing rotational motion are [lat...
Question: C.1.1

## Apply Euler’s method to the equations of motion (5.86) for an electromechanical device. ...

We reduce Eq. (5.86) to a set of algebraic equatio...
Question: A.6.3

## Consider a vector A = Ax x + Ay y +Az z at a point (x, y, z) in Cartesian coordinates. Determine its location and representation in spherical coordinates. ...

From Table A.3 the location of (x, y, z) is [latex...
Question: A.6.2

## Consider a vector A = Ars rs + Aθ θ + AΦ Φ at a point (rs, θ, Φ) in spherical coordinates. Determine its location and representation in cylindrical coordinates. ...

From Table A.2 the location of (r_{s}[/late...
Question: A.6.1

## Consider a vector A = Arc rc + AΦ Φ + Az z at a point (rc, Φ, z) in cylindrical coordinates. Determine its location and representation in Cartesian coordinates. ...

From Table A.1 the location in Cartesian coordinat...
Question: A.5.2

## Verify the Divergence theorem for the vector field A(x, y) = αrr + βzz where V and S are the volume and surface of the cylinder shown in Fig. A.8. Here, α and β are constants. ...

We have already evaluated \oint_{s} A· \hat...
Question: A.5.1

## Verify Stokes’ theorem for the vector field A(x, y) = (2x – y)x – yz^2y + y^2zz where S is the half-surface of the sphere x^2 + y^2 + z^2 = a^2 and C is its bounding curve in the x-y plane (Fig. A.10). ...

First, we evaluate \int_{s} (∇×A) · \hat{n}...
Question: 5.15.1

## Derive the equations of motion for the actuator shown in Fig. 5.53. ...

This is a moving magnet actuator and its behavior ...
Question: A.4.3

## Evaluate the integral ∮s A· ds where A(x, y) = αrr + βzz, and S is the closed surface of the cylinder shown in Fig. A.8. Here, α and β are constants. ...

Along path 1 we have \int_{C_{1}} A(x,y)⋅dl...