This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
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5 | substitute LHS of expr 1 into expr 2 |
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LHS diff is nabla**2*(pdg2718(pdg1467*pdg2321*pdg4621) - exp(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472) RHS diff is partial*pdg6197*pdg7940*(pdg2718(pdg1467*pdg2321*pdg4621) - exp(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472)/pdg1467**2 |
9499428242:
9394939493: 2029293929: |
9499428242:
9394939493: 2029293929: |
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6 | differentiate with respect to |
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no check performed |
2029293929:
4985825552: |
2029293929:
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2 | declare initial expr |
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no validation is available for declarations |
8572852424:
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8572852424:
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3 | declare guess solution |
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no validation is available for declarations |
8494839423:
9499428242: |
8494839423:
9499428242: |
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4 | substitute LHS of expr 1 into expr 2 |
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valid |
8572852424:
8494839423: 9394939493: |
8572852424:
8494839423: 9394939493: |
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7 | differentiate with respect to |
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no check performed |
4985825552:
1858578388: |
4985825552:
1858578388: |
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10 | simplify |
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LHS diff is nabla**2*(pdg2718(pdg1467*pdg2321*pdg4621) - 1)*pdg6238(pdg9472) RHS diff is pdg2321**2*(1 - pdg2718(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472)/pdg4567**2 |
9485384858:
3485475729: |
9485384858:
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11 | declare final expr |
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no validation is available for declarations |
3485475729:
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9 | substitute LHS of expr 1 into expr 2 |
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LHS diff is -nabla**2*pdg2718(pdg1467*pdg2321*pdg4621)*pdg6238(pdg9472) + pdg6197*pdg7940 RHS diff is (pdg2321**2*pdg2718(pdg1467*pdg2321*pdg4621)*pdg6238(pdg9472) + 1)/pdg4567**2 |
1858578388:
4585828572: failed 9485384858: |
1858578388:
4585828572: N/A 9485384858: |
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1 | declare initial expr |
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no validation is available for declarations |
8494839423:
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8 | declare initial expr |
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no validation is available for declarations |
4585828572:
failed |
4585828572:
N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
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6197 | constant |
\mu_0
\(\mu_0\) |
real |
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vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant |
1.25663706212E^{-6} N/A^2 |
8 | ||
7940 | constant |
\epsilon_0
\(\epsilon_0\) |
real |
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vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum |
8.8541878128E-{12} F/m |
14 | ||
2718 | constant |
\exp
\(\exp\) |
['real'] | dimensionless | e |
2.71828 unitless |
8 | ||
1467 | variable |
t
\(t\) |
['real'] |
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time |
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121 | ||
9472 | variable |
\vec{r}
\(\vec{r}\) |
real |
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radius vector |
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24 | ||
4567 | constant |
c
\(c\) |
['real'] |
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speed of light in vacuum |
299792458 meters/second |
32 | ||
4621 | variable |
i
\(i\) |
['imaginary'] | dimensionless | imaginary unit |
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74 | ||
4326 | variable |
\vec{E}
\(\vec{E}\) |
complex | dimensionless | electric field | 9 | |||
6238 | variable |
E
\(E\) |
real | dimensionless | electric field | 20 | |||
2321 | variable |
\omega
\(\omega\) |
['real'] |
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angular frequency | 26 |