Calculating Total Charge: Charge is continuously distributed on a torus given by the density, rho_(vg)=rho_(0)((t)/((A)))cos(alpha)cos(3beta) The torus is centred in the (xy)-plane and parameterized with (t,alpha,beta) as shown. t is the radial distance from the central ring of the torus. t in(0,A) alpha is the angle from the (xy)-plane about the c solutionspile.com

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Calculating Total Charge: Charge is continuously distributed on a torus given by the density, rho_(vg)=rho_(0)((t)/((A)))cos(alpha)cos(3beta) The torus is centred in the (xy)-plane and parameterized with (t,alpha,beta) as shown. t is the radial distance from the central ring of the torus. t in(0,A) alpha is the angle from the (xy)-plane about the central ring of the torus. alpha in[0,2pi] beta is the azimuthal angle - defined the same as with cylindrical and spherical coordinates. beta in[0,2pi] Using cylindrical coordinates, express the following in terms of the parameterization. a) The source position coordinates. b) The tangent vectors, d vec(T)_(1),d vec(T)_(alpha),&d vec(T)_(beta) c) The volume element. d) The triple integral to calculate the total

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6) Calculating Total Charge: Charge is continuously distributed on a torus given by the density,

?_{vg} = ?_{0} (\frac{t}{A}) cos (?) cos (3 ?)

The torus is centred in the (xy)-plane and parameterized with

(t, ?, ?)

as shown. -

t

is the radial distance from the central ring of the torus.

t ? (0, A)

-

?

is the angle from the (xy)-plane about the central ring of the torus.

? ? [0, 2 ?]

-

?

is the azimuthal angle - defined the same as with cylindrical and spherical coordinates.

? ? [0, 2 ?]

Using cylindrical coordinates, express the following in terms of the parameterization. a) The source position coordinates. b) The tangent vectors,

d T_{t}, d T_{?}, & d T_{?}

c) The volume element. d) The triple integral to calculate the total charge. e) Calculate the total charge. (it's not as scary as it looks)

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