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| − | ====Check of Total Magnitude #1: Doesn't work====
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| − | :<math>
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| − | \begin{alignat}{2}
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| − | \left ( \frac{q}{k} \right )^2 d^{\prime 2}
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| − | & = \begin{alignat}{2} [ & \left( x \cos \phi_g -\sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) \right)^2 \\ & + \left( x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} \right)^2 \\ & + \left( d \sin \theta_g + z \cos \theta_g \right)^2 ] \end{alignat} \\
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| − | & = \begin{alignat}{2} [
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| − | & x^2 \cos^2 \phi_g - x \cos \phi_g \sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) + \sin^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 \\
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| − | & + x^2 \sin^2 \phi_g + x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} x \sin \phi_g \\
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| − | & + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g )x \sin \phi_g + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \\
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| − | & - d^{\prime} x \sin \phi_g - d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
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| − | & + d^2 \sin^2 \theta_g + 2 d \sin \theta_g z \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
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| − |
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| − | & = \begin{alignat}{2} [
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| − | & x^2 \cos^2 \phi_g - x \cos \phi_g \sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) + \sin^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 \\
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| − | & + x^2 \sin^2 \phi_g + 2 x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - 2 d^{\prime} x \sin \phi_g \\
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| − | & + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - 2 d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
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| − | & + d^2 \sin^2 \theta_g + 2 d \sin \theta_g z \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
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| − |
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| − | & = \begin{alignat}{2} [
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| − | & x^2 - x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + ( d \cos \theta_g - z \sin \theta_g )^2 \\
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| − | & + 2 x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - 2 d^{\prime} x \sin \phi_g \\
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| − | & - 2 d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
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| − | & + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
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| − |
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| − | & = \begin{alignat}{2} [
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| − | & x^2 + d^2 \cos^2 \theta_g - 2 dz \cos \theta_g \sin \theta_g + z^2 \sin^2 \theta_g \\
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| − | & + ( - x \sin \phi_g \cos \phi_g + 2 x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\
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| − | & - 2 d^{\prime} x \sin \phi_g \\
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| − | & + d^{\prime 2} \\
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| − | & + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
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| − |
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| − | & = \begin{alignat}{2} [
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| − | & d^{\prime 2} + x^2 + d^2 + z^2 - 2 dz \cos \theta_g \sin \theta_g \\
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| − | & + ( x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\
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| − | & + 2 d z \sin \theta_g \cos \theta_g - 2 d^{\prime} x \sin \phi_g ] \end{alignat} \\
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| − |
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| − | & = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\
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| − |
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| − | & = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin \phi_g - 2 d^{\prime} )\cos \phi_g( d \cos \theta_g - z \sin \theta_g ) \\
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| − |
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| − |
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| − | & = ? \\
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| − | & = ? \\
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| − | & = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + 2 d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \\
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| − | & = 2 d^{\prime} \left( d^{\prime} - x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \right) \\
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| − | \left( \frac{q}{k} \right)^2
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| − | & = 2 \left( 1 - \frac{x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g )}{d^{\prime} } \right)
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| − | \end{alignat}
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| − | </math>
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