Finding a Vector PotentialJSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 8-9</Text-field>JSFH
Use 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 to obtain a vector potential for 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.
InitializeTools\342\211\273Load Package: Student Vector Calculuswith(Student:-VectorCalculus):JSFHSet the display format for vectors.Tools\342\211\273Tasks\342\211\273Browse:
Calculus - Vector\342\211\273Vector Algebra and Settings
Display Format for Vectorsuse DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
module()
local q;
Do(%RadioButton12(visible)=true);
Do(%RadioButton13(visible)=true);
Do(%Button15(visible)=true);
q := VectorCalculus:-BasisFormat();
if q=false then Do(%RadioButton12 = true);
else Do(%RadioButton13 = true);
end if;
end module;
end use;
use DocumentTools, VectorCalculus in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%RadioButton12) then BasisFormat(false);
else BasisFormat(true); end if;
end use;
use DocumentTools, VectorCalculus in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%RadioButton13) then BasisFormat(true);
else BasisFormat(false); end if;
end use;
use DocumentTools,VectorCalculus in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%RadioButton12) then BasisFormat(false);
else BasisFormat(true); end if;
Do(%RadioButton12(visible)=false);
Do(%RadioButton13(visible)=false);
Do(%Button15(visible)=false);
end use;
%;Define the vector field FDefine F as a VectorField.
Press the Enter key.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 a vector potential for FType F and press the Enter key.Context Menu: Vector PotentialContext Menu: Assign to a Name\342\211\273ALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Apply the formula 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 Menu: Assign 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Context Menu: Assign 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Context Menu: Assign 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Write the vector of integrals for A.
Press the Enter key.Context Menu:
Evaluate at a Point\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJjRidGL0YyRjUtSSNtbkdGJDYkUSIwRidGOUY5Context Menu: Assign to a Name\342\211\273BLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Investigate the non-uniqueness in the vector potentialForm the difference of the two vector potentials.
Press the Enter key.Context Menu: Scalar 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