ω = ω 0 {\displaystyle \omega =\omega _{0}}
T = ϵ 0 π r 2 γ 2 2 ( V d ) 2 {\displaystyle T={\frac {\epsilon _{0}\pi r^{2}\gamma ^{2}}{2}}{\Bigg (}{\frac {V}{d}}{\Bigg )}^{2}}
γ = L ( 1 + d r ) d + L {\displaystyle \gamma ={\frac {L(1+{\frac {d}{r}})}{d+L}}}
a 1 = a 2 c o s h ( k L ) + c o s ( k L ) s i n ( k L ) − s i n h ( k L ) {\displaystyle a_{1}=a_{2}{\frac {cosh(kL)+cos(kL)}{sin(kL)-sinh(kL)}}}
0 = a 2 c o s h ( k L ) + c o s ( k L ) s i n ( k L ) − s i n h ( k L ) c o s h ( k L ) + a 2 s i n h ( k x ) + a 2 c o s h ( k L ) + c o s ( k L ) s i n ( k L ) − s i n h ( k L ) c o s ( k x ) + a 2 s i n ( k x ) {\displaystyle 0=a_{2}{\frac {cosh(kL)+cos(kL)}{sin(kL)-sinh(kL)}}cosh(kL)+a_{2}sinh(kx)+a_{2}{\frac {cosh(kL)+cos(kL)}{sin(kL)-sinh(kL)}}cos(kx)+a_{2}sin(kx)}
0 = ( c o s h ( k L ) + c o s ( k L ) ) ( c o s h ( k L ) + c o s ( k L ) ) s i n ( k L ) − s i n h ( k L ) + ( s i n ( k L ) + s i n h ( k L ) ) ( s i n ( k L ) − s i n h ( k L ) ) s i n ( k L ) − s i n h ( k L ) {\displaystyle 0={\frac {(cosh(kL)+cos(kL))(cosh(kL)+cos(kL))}{sin(kL)-sinh(kL)}}+{\frac {(sin(kL)+sinh(kL))(sin(kL)-sinh(kL))}{sin(kL)-sinh(kL)}}}
0 = c o s h 2 ( k L ) + 2 c o s ( k L ) c o s h ( k L ) + c o s 2 ( k L ) + s i n 2 ( k L ) − s i n h 2 ( k L ) s i n ( k L ) − s i n h ( k L ) = 2 c o s ( k L ) c o s h ( k L ) + 2 s i n ( k L ) − s i n h ( k L ) {\displaystyle 0={\frac {cosh^{2}(kL)+2cos(kL)cosh(kL)+cos^{2}(kL)+sin^{2}(kL)-sinh^{2}(kL)}{sin(kL)-sinh(kL)}}={\frac {2cos(kL)cosh(kL)+2}{sin(kL)-sinh(kL)}}}
0 = 2 c o s ( k L ) c o s h ( k L ) + 2 = c o s ( k L ) c o s h ( k L ) + 1 {\displaystyle 0=2cos(kL)cosh(kL)+2=cos(kL)cosh(kL)+1\,\!}
u ( 0 ) = u ′ ( 0 ) = u ″ ( L ) = u ‴ ( L ) = 0 {\displaystyle u(0)=u'(0)=u''(L)=u'''(L)=0\,\!}
u ( x ) = a 1 c o s h ( k x ) + a 2 s i n h ( k x ) + a 3 c o s ( k x ) + a 4 s i n ( k x ) {\displaystyle u(x)=a_{1}cosh(kx)+a_{2}sinh(kx)+a_{3}cos(kx)+a_{4}sin(kx)\,\!}
u ′ ( x ) = k a 1 s i n h ( k x ) + k a 2 c o s h ( k x ) − k a 3 s i n ( k x ) + k a 4 c o s ( k x ) {\displaystyle u'(x)=ka_{1}sinh(kx)+ka_{2}cosh(kx)-ka_{3}sin(kx)+ka_{4}cos(kx)\,\!}
u ″ ( x ) = k 2 a 1 c o s h ( k x ) + k 2 a 2 s i n h ( k x ) − k 2 a 3 c o s ( k x ) − k 2 a 4 s i n ( k x ) {\displaystyle u''(x)=k^{2}a_{1}cosh(kx)+k^{2}a_{2}sinh(kx)-k^{2}a_{3}cos(kx)-k^{2}a_{4}sin(kx)\,\!}
u ‴ ( x ) = k 3 a 1 s i n h ( k x ) + k 3 a 2 c o s h ( k x ) + k 3 a 3 s i n ( k x ) − k 3 a 4 c o s ( k x ) {\displaystyle u'''(x)=k^{3}a_{1}sinh(kx)+k^{3}a_{2}cosh(kx)+k^{3}a_{3}sin(kx)-k^{3}a_{4}cos(kx)\,\!}
ρ A ∂ 2 ∂ t 2 Z ( x , t ) + E I ∂ 4 ∂ x 4 Z ( x , t ) − T ∂ 2 ∂ x 2 Z ( x , t ) = 0 {\displaystyle \rho A{\frac {\partial ^{2}}{\partial t^{2}}}Z(x,t)+EI{\frac {\partial ^{4}}{\partial x^{4}}}Z(x,t)-T{\frac {\partial ^{2}}{\partial x^{2}}}Z(x,t)=0}
Z ( x , t ) = u ( x ) e i ω t {\displaystyle Z(x,t)=u(x)e^{i\omega t}\,\!}
∂ 2 ∂ t 2 Z ( x , t ) = − ω 2 u ( x ) e i ω t {\displaystyle {\frac {\partial ^{2}}{\partial t^{2}}}Z(x,t)=-\omega ^{2}u(x)e^{i\omega t}}
∂ 2 ∂ x 2 Z ( x , t ) = e i ω t d d x 2 u ( x ) {\displaystyle {\frac {\partial ^{2}}{\partial x^{2}}}Z(x,t)=e^{i\omega t}{\frac {d}{dx^{2}}}u(x)}
∂ 4 ∂ x 4 Z ( x , t ) = e i ω t d d x 4 u ( x ) {\displaystyle {\frac {\partial ^{4}}{\partial x^{4}}}Z(x,t)=e^{i\omega t}{\frac {d}{dx^{4}}}u(x)}
− ρ A ω 2 u ( x ) e i ω t + E I e i ω t d d x 2 u ( x ) − T e i ω t d d x 2 u ( x ) = 0 {\displaystyle -\rho A\omega ^{2}u(x)e^{i\omega t}+EIe^{i\omega t}{\frac {d}{dx^{2}}}u(x)-Te^{i\omega t}{\frac {d}{dx^{2}}}u(x)=0}
− ρ A ω 2 u ( x ) + E I d 4 d x 4 u ( x ) − T d 2 d x 2 u ( x ) = 0 {\displaystyle -\rho A\omega ^{2}u(x)+EI{\frac {d^{4}}{dx^{4}}}u(x)-T{\frac {d^{2}}{dx^{2}}}u(x)=0}
u ( x ) = e k x {\displaystyle u(x)=e^{kx}\,\!}
E I k 4 e k x − T k 2 e k x − ρ A ω 2 e k x = 0 {\displaystyle EIk^{4}e^{kx}-Tk^{2}e^{kx}-\rho A\omega ^{2}e^{kx}=0\,\!}
E I k 4 − T k 4 − ρ A ω 2 = 0 {\displaystyle EIk^{4}-Tk^{4}-\rho A\omega ^{2}=0\,\!}
k 2 = T + T 2 + 4 E I ρ A ω 2 2 E I {\displaystyle k^{2}={\frac {T+{\sqrt {T^{2}+4EI\rho A\omega ^{2}}}}{2EI}}\,\!}
c = ω m ″ B ″ 4 {\displaystyle c={\sqrt {\omega }}{\sqrt[{4}]{\frac {m''}{B''}}}}
B ″ = h 3 E 12 ( 1 − ν 2 ) {\displaystyle B''={\frac {h^{3}E}{12(1-\nu ^{2})}}}
m ″ = ρ h {\displaystyle m''=\rho h\,\!}
c = ω E h 2 12 ρ ( 1 − ν 2 ) 4 {\displaystyle c={\sqrt {\omega }}{\sqrt[{4}]{\frac {Eh^{2}}{12\rho (1-\nu ^{2})}}}}
h = c 2 ω 12 ρ ( 1 − ν 2 ) E = c 2 2 π f 12 ρ ( 1 − ν 2 ) E {\displaystyle h={\frac {c^{2}}{\omega }}{\sqrt {\frac {12\rho (1-\nu ^{2})}{E}}}={\frac {c^{2}}{2\pi f}}{\sqrt {\frac {12\rho (1-\nu ^{2})}{E}}}}
c 2 2 π f {\displaystyle {\frac {c^{2}}{2\pi f}}}
c B = B ′ ω 2 m ″ 4 {\displaystyle c_{B}={\sqrt[{4}]{\frac {B'\omega ^{2}}{m''}}}}
F = q ( E + v × B ) = q E + q ( v × B ) {\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B} )=q\mathbf {E} +q(\mathbf {v} \times \mathbf {B} )}
F = q ( v × B ) = l ( I × B ) {\displaystyle \mathbf {F} =q(\mathbf {v} \times \mathbf {B} )=l(\mathbf {I} \times \mathbf {B} )}
× {\displaystyle \times }
a × b = c {\displaystyle \mathbf {a} \times \mathbf {b} =\mathbf {c} }
n ^ {\displaystyle \mathbf {\hat {n}} }
a ⋅ b = c {\displaystyle \mathbf {a} \cdot \mathbf {b} =c}
a = [ x a y a z a ] , b = [ x b y b z b ] , c = a + b = [ x a y a z a ] + [ x b y b z b ] = [ x a + x b y a + y b z a + y c ] {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},\mathbf {b} ={\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}},\mathbf {c} =\mathbf {a} +\mathbf {b} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}}+{\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}}={\begin{bmatrix}x_{a}+x_{b}\\y_{a}+y_{b}\\z_{a}+y_{c}\\\end{bmatrix}}}
a = [ x a y a z a ] , − a = [ − x a − y a − z a ] {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},-\mathbf {a} ={\begin{bmatrix}-x_{a}\\-y_{a}\\-z_{a}\\\end{bmatrix}}}
a = [ x a y a z a ] , b = [ x b y b z b ] , c = a − b = [ x a y a z a ] − [ x b y b z b ] = [ x a − x b y a − y b z a − y c ] {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},\mathbf {b} ={\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}},\mathbf {c} =\mathbf {a} -\mathbf {b} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}}-{\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}}={\begin{bmatrix}x_{a}-x_{b}\\y_{a}-y_{b}\\z_{a}-y_{c}\\\end{bmatrix}}}
a = [ x a y a z a ] , ‖ a ‖ = x a 2 + y a 2 + z a 2 {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},\left\|\mathbf {a} \right\|={\sqrt {{x_{a}}^{2}+{y_{a}}^{2}+{z_{a}}^{2}}}}
a = [ x a y a z a ] , b = [ x b y b z b ] , a ⋅ b = ‖ a ‖ ‖ b ‖ cos θ = x a x b + y a y b + z a z b {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},\mathbf {b} ={\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}},\mathbf {a} \cdot \mathbf {b} =\left\|\mathbf {a} \right\|\left\|\mathbf {b} \right\|\cos \theta =x_{a}x_{b}+y_{a}y_{b}+z_{a}z_{b}}
a = [ x a y a z a ] = ( x a , y a , z a ) {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}}=\left(x_{a},y_{a},z_{a}\right)}
a x = x a x ^ = [ x a 0 0 ] , a y = y a y ^ = [ 0 y a 0 ] , a z = z a z ^ = [ 0 0 z a ] {\displaystyle \mathbf {a_{x}} =x_{a}\mathbf {\hat {x}} ={\begin{bmatrix}x_{a}\\0\\0\\\end{bmatrix}},\mathbf {a_{y}} =y_{a}\mathbf {\hat {y}} ={\begin{bmatrix}0\\y_{a}\\0\\\end{bmatrix}},\mathbf {a_{z}} =z_{a}\mathbf {\hat {z}} ={\begin{bmatrix}0\\0\\z_{a}\\\end{bmatrix}}}
x ^ = [ 1 0 0 ] , y ^ = [ 0 1 0 ] , z ^ = [ 0 0 1 ] {\displaystyle \mathbf {\hat {x}} ={\begin{bmatrix}1\\0\\0\\\end{bmatrix}},\mathbf {\hat {y}} ={\begin{bmatrix}0\\1\\0\\\end{bmatrix}},\mathbf {\hat {z}} ={\begin{bmatrix}0\\0\\1\\\end{bmatrix}}}
c a = [ c x a c y a c z a ] {\displaystyle c\mathbf {a} ={\begin{bmatrix}cx_{a}\\cy_{a}\\cz_{a}\\\end{bmatrix}}}
a = [ x a y a z a ] , b = [ x b y b z b ] , a × b = [ y a z b − y b z a z a x b − z b x a x a y b − x b y a ] = n ^ ‖ a ‖ ‖ b ‖ sin θ {\displaystyle \mathbf {a} ={\begin{bmatrix}x_{a}\\y_{a}\\z_{a}\\\end{bmatrix}},\mathbf {b} ={\begin{bmatrix}x_{b}\\y_{b}\\z_{b}\\\end{bmatrix}},\mathbf {a} \times \mathbf {b} ={\begin{bmatrix}y_{a}z_{b}-y_{b}z_{a}\\z_{a}x_{b}-z_{b}x_{a}\\x_{a}y_{b}-x_{b}y_{a}\\\end{bmatrix}}=\mathbf {\hat {n}} \left\|\mathbf {a} \right\|\left\|\mathbf {b} \right\|\sin \theta }
a = x a x ^ + y a y ^ + z a z ^ {\displaystyle \mathbf {a} =x_{a}\mathbf {\hat {x}} +y_{a}\mathbf {\hat {y}} +z_{a}\mathbf {\hat {z}} }
B = [ B x B y B z ] , ∂ B ∂ x = [ ∂ B x ∂ x ∂ B y ∂ x ∂ B Z ∂ x ] {\displaystyle \mathbf {B} ={\begin{bmatrix}B_{x}\\B_{y}\\B_{z}\\\end{bmatrix}},{\frac {\partial \mathbf {B} }{\partial x}}={\begin{bmatrix}{\frac {\partial B_{x}}{\partial x}}\\{\frac {\partial B_{y}}{\partial x}}\\{\frac {\partial B_{Z}}{\partial x}}\\\end{bmatrix}}}
∫ A B f ⋅ d s {\displaystyle \int _{AB}\mathbf {f} \ \cdot d\mathbf {s} }
∮ C f ⋅ d s {\displaystyle \oint _{C}\mathbf {f} \ \cdot d\mathbf {s} }
∭ V F d V {\displaystyle \iiint \limits _{V}\mathbf {F} \ dV}
∬ S ⊂ ⊃ F ⋅ d S {\displaystyle \iint \limits _{S}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset \mathbf {F} \ \cdot d\mathbf {S} }
∬ S F ⋅ d S {\displaystyle \iint \limits _{S}\mathbf {F} \ \cdot d\mathbf {S} }
∇ = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) {\displaystyle \nabla =\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right)}
F → {\displaystyle {\vec {F}}}
y F {\displaystyle y_{F}\,\!}
F y {\displaystyle F_{y}\,\!}
div F = ∂ F x ∂ x + ∂ F y ∂ y + ∂ F z ∂ z {\displaystyle \operatorname {div} F={\frac {\partial F_{x}}{\partial x}}+{\frac {\partial F_{y}}{\partial y}}+{\frac {\partial F_{z}}{\partial z}}}
div F = ∇ ⋅ F = [ ∂ ∂ x ∂ ∂ y ∂ ∂ z ] ⋅ [ F x F y F z ] = ∂ F x ∂ x + ∂ F y ∂ y + ∂ F z ∂ z {\displaystyle \operatorname {div} \,\mathbf {F} =\nabla \cdot \mathbf {F} ={\begin{bmatrix}{\frac {\partial }{\partial x}}\\{\frac {\partial }{\partial y}}\\{\frac {\partial }{\partial z}}\\\end{bmatrix}}\cdot {\begin{bmatrix}F_{x}\\F_{y}\\F_{z}\\\end{bmatrix}}={\frac {\partial F_{x}}{\partial x}}+{\frac {\partial F_{y}}{\partial y}}+{\frac {\partial F_{z}}{\partial z}}}
curl F = ( ∂ F z ∂ y − ∂ F y ∂ z ) x ^ + ( ∂ F x ∂ z − ∂ F z ∂ x ) y ^ + ( ∂ F y ∂ x − ∂ F x ∂ y ) z ^ {\displaystyle \operatorname {curl} \ \mathbf {F} =\left({\frac {\partial F_{z}}{\partial y}}-{\frac {\partial F_{y}}{\partial z}}\right)\mathbf {\hat {x}} +\left({\frac {\partial F_{x}}{\partial z}}-{\frac {\partial F_{z}}{\partial x}}\right)\mathbf {\hat {y}} +\left({\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}\right)\mathbf {\hat {z}} }
curl F = ∇ × F = [ ∂ ∂ x ∂ ∂ y ∂ ∂ z ] × [ F x F y F z ] = {\displaystyle \operatorname {curl} \ \mathbf {F} =\nabla \times \mathbf {F} ={\begin{bmatrix}{\frac {\partial }{\partial x}}\\{\frac {\partial }{\partial y}}\\{\frac {\partial }{\partial z}}\\\end{bmatrix}}\times {\begin{bmatrix}F_{x}\\F_{y}\\F_{z}\\\end{bmatrix}}=} ( ∂ F z ∂ y − ∂ F y ∂ z ) x ^ + ( ∂ F x ∂ z − ∂ F z ∂ x ) y ^ + ( ∂ F y ∂ x − ∂ F x ∂ y ) z ^ {\displaystyle \left({\frac {\partial F_{z}}{\partial y}}-{\frac {\partial F_{y}}{\partial z}}\right)\mathbf {\hat {x}} +\left({\frac {\partial F_{x}}{\partial z}}-{\frac {\partial F_{z}}{\partial x}}\right)\mathbf {\hat {y}} +\left({\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}\right)\mathbf {\hat {z}} }
∭ V ( ∇ ⋅ F ) d V = ∬ S ⊂ ⊃ F ⋅ d S {\displaystyle \iiint \limits _{V}\left(\nabla \cdot \mathbf {F} \right)dV=\iint \limits _{S}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset \mathbf {F} \cdot d\mathbf {S} }
∬ S ( ∇ × F ) d S = ∮ s F d s {\displaystyle \iint \limits _{S}\left(\nabla \times \mathbf {F} \right)dS=\oint \limits _{s}\mathbf {F} \ ds}
grad f = ( ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z ) {\displaystyle \operatorname {grad} \ f=\left({\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}\right)}
grad f = ∇ f = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) f = ( ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z ) {\displaystyle \operatorname {grad} \ f=\nabla f=\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right)f=\left({\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}\right)}
B ⋅ d ℓ = B d ℓ {\displaystyle \mathbf {B} \cdot d{\boldsymbol {\ell }}=Bd\ell }
∮ C B ⋅ d ℓ = ∮ C B d ℓ = 2 π r B = μ 0 I e n c {\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\oint _{C}Bd\ell =2\pi rB=\mu _{0}I_{\mathrm {enc} }}
B = μ 0 I e n c 2 π r {\displaystyle B={\frac {\mu _{0}I_{\mathrm {enc} }}{2\pi r}}}
N = m × B {\displaystyle \mathbf {N} =\mathbf {m} \times \mathbf {B} }
m = I a {\displaystyle \mathbf {m} =I\mathbf {a} }
F = 2 π r I B r {\displaystyle F=2\pi rIB_{r}\,\!}
2 π r B r Δ z {\displaystyle 2\pi rB_{r}\Delta z\,\!}
π r 2 ( − B z ( z ) + B z ( z + Δ z ) = π r 2 ( ∂ B z ∂ z ) Δ z {\displaystyle \pi r^{2}(-B_{z}(z)+B_{z}(z+\Delta z)=\pi r^{2}({\frac {\partial B_{z}}{\partial z}})\Delta z}
2 π r B r Δ z + π r 2 ( ∂ B z ∂ z ) Δ z = 0 {\displaystyle 2\pi rB_{r}\Delta z+\pi r^{2}({\frac {\partial B_{z}}{\partial z}})\Delta z=0}
B r = − r 2 ∂ B z ∂ z {\displaystyle B_{r}=-{\frac {r}{2}}{\frac {\partial B_{z}}{\partial z}}}
F = 2 π r I r 2 ∂ B z ∂ z = π r 2 I ∂ B z ∂ z {\displaystyle F=2\pi rI{\frac {r}{2}}{\frac {\partial B_{z}}{\partial z}}=\pi r^{2}I{\frac {\partial B_{z}}{\partial z}}}
F = m ∂ B z ∂ z {\displaystyle F=m{\frac {\partial B_{z}}{\partial z}}}
F x = m ⋅ grad B x {\displaystyle F_{x}=\mathbf {m} \cdot \operatorname {grad} \ B_{x}}
m = I A = M d a d z {\displaystyle m=I\ A=M\ da\ dz}
∮ C B ⋅ d ℓ = B a s L p a d = μ 0 I e n c {\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=B_{as}L_{pad}=\mu _{0}I_{\mathrm {enc} }}
B a s L p a d = μ 0 I e n c = μ 0 N p a d I s p o e l {\displaystyle B_{as}L_{pad}=\mu _{0}I_{\mathrm {enc} }=\mu _{0}N_{pad}I_{spoel}\,\!}
n = N s p o e l L s p o e l {\displaystyle n={\frac {N_{spoel}}{L_{spoel}}}}
N p a d = N s p o e l L s p o e l L p a d = n L p a d {\displaystyle N_{pad}={\frac {N_{spoel}}{L_{spoel}}}L_{pad}=nL_{pad}}
B a s L p a d = μ 0 N p a d I s p o e l = μ 0 n L p a d I s p o e l {\displaystyle B_{as}L_{pad}=\mu _{0}N_{pad}I_{spoel}=\mu _{0}nL_{pad}I_{spoel}\,\!}
B a s = μ n I s p o e l = μ N s p o e l L s p o e l I s p o e l {\displaystyle B_{as}=\mu nI_{spoel}=\mu {\frac {N_{spoel}}{L_{spoel}}}I_{spoel}}
P = I 2 R {\displaystyle P=I^{2}R\,\!}
I = q t {\displaystyle I={\frac {q}{t}}}
Φ B , S = ∬ S B ⋅ d S {\displaystyle \Phi _{B,S}=\iint \limits _{S}\mathbf {B} \ \cdot d\mathbf {S} }
F x = m z ∂ B x ∂ z {\displaystyle F_{x}=m_{z}{\frac {\partial B_{x}}{\partial z}}}
∂ B x ∂ z {\displaystyle {\frac {\partial B_{x}}{\partial z}}}