{"id":11444,"date":"2024-11-12T12:52:35","date_gmt":"2024-11-12T12:52:35","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11444"},"modified":"2024-12-03T14:37:48","modified_gmt":"2024-12-03T14:37:48","slug":"superficies-equipotenciais-trabalho-da-forca-eletrostatica-en","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrostatica\/superficies-equipotenciais-trabalho-da-forca-eletrostatica-en\/","title":{"rendered":"Equipotential Surfaces \u2013 Work of the Electrostatic Force EN"},"content":{"rendered":"

EQUIPOTENTIAL SURFACES \u2013 WORK OF THE ELECTROSTATIC FORCE<\/span><\/h1>\n
\n

Equipotential Surfaces \u2013 Work of the Electrostatic Force<\/span><\/b><\/p>\n

<\/b>The equipotential surface of an electric field\u00a0<\/span><\/b>is defined\u00a0<\/b><\/span>as\u00a0<\/span><\/b>any surface at whose points the\u00a0<\/span><\/b>electric potential is constant.<\/span><\/b><\/p>\n

These surfaces have two important properties:<\/span>
\n<\/b><\/p>\n

\"\"\u00a0The\u00a0<\/span><\/b>electric force during the displacement of a point electric charge over an equipotential surface is zero.<\/span><\/b><\/p>\n

Equipotential surfaces\u00a0<\/span><\/b>are perpendicular to the lines of force or electric field lines\u00a0<\/span><\/b>and, consequently,\u00a0<\/span><\/b>perpendicular to the electric field vector.\u00a0<\/span>\"\"<\/b><\/p>\n

 <\/p>\n

Equipotential surfaces and lines of force of a point charge Q<\/span><\/b><\/p>\n

In the\u00a0<\/span><\/b>particular case of the field of a point charge Q\u00a0<\/span><\/b>,\u00a0<\/span><\/b>symmetry\u00a0<\/span><\/b>suggests that the\u00a0<\/span><\/b>equipotential surfaces\u00a0<\/span><\/b>are\u00a0<\/span><\/b>spherical surfaces concentric\u00a0<\/span><\/b>with the\u00a0<\/span><\/b>charge Q\u00a0<\/span><\/b>and the\u00a0<\/span><\/b>(field) lines of force are radial with the center of the charge.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Note in the\u00a0<\/span><\/b>figures above\u00a0<\/span><\/b>that the\u00a0<\/span><\/b>lines of force (field)\u00a0<\/span><\/b>move\u00a0<\/span><\/b>away\u00a0<\/span><\/b>from the\u00a0<\/span><\/b>positive charges\u00a0<\/span><\/b>and in the\u00a0<\/span><\/b>figures below\u00a0<\/span><\/b>they\u00a0<\/span><\/b>move closer\u00a0<\/span><\/b>to the\u00a0<\/span><\/b>negative ones.<\/span><\/b><\/p>\n

\"\"<\/p>\n

For\u00a0<\/span><\/b>positive charges, the\u00a0<\/span><\/b>potential of each surface\u00a0<\/span><\/b>increases\u00a0<\/b>as it\u00a0<\/b>approaches the charge\u00a0<\/b>and for\u00a0<\/b>negative charges it decreases as it moves away from the charge.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

 <\/p>\n

The figures below represent several configurations with their respective lines of force and equipotential surfaces.<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Equipotential Surfaces of a\u00a0<\/span><\/b>Uniform Electric Field<\/span><\/b><\/p>\n

 <\/p>\n

A uniform electric field\u00a0<\/span><\/b>has the same intensity, direction and sense at all its infinite points and is\u00a0<\/span><\/b>obtained between two identical\u00a0<\/span><\/b>and parallel\u00a0<\/b><\/span>conductive plates\u00a0<\/span><\/b>electrified with charges of the same magnitude but opposite signs.<\/b><\/span><\/b><\/b><\/p>\n

\"\"<\/p>\n

Note, in the figure above,\u00a0<\/span><\/b>that in this case the\u00a0<\/span><\/b>equipotential surfaces are flat and parallel to each other.<\/span><\/b><\/p>\n

 <\/p>\n

Work (W) and potential difference (U)<\/span><\/b><\/p>\n

 <\/p>\n

Consider the\u00a0<\/span><\/b>electric field created by a point source charge Q (figure I)\u00a0<\/span><\/b>and the uniform\u00a0<\/span><\/b>electric field\u00a0<\/span><\/b>created by two identical, parallel conductive plates electrified with charges of\u00a0<\/b>the same magnitude but opposite signs (figure II).<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

A\u00a0<\/span><\/b>test particle q,\u00a0<\/span><\/b>left inside these fields, is subject to a force\u00a0\u00a0<\/b>, which makes it move from point R (with potential VR\u00a0<\/b>)<\/b><\/sub>\u00a0to point S (with potential V\u00a0<\/b>S<\/b><\/sub>\u00a0).<\/b><\/span>\u00a0<\/b>\"\"<\/b><\/b><\/b><\/b><\/b><\/p>\n

Figure I\u00a0<\/span><\/b>variable electric field\u00a0<\/b>\u00a0 being the\u00a0<\/b>\u00a0conservative\u00a0<\/b>force\u00a0\u00a0<\/b>, the\u00a0<\/b>work\u00a0<\/b>done by it is provided by the\u00a0<\/b>variation\u00a0<\/b>of electric potential energy (initial minus final)\u00a0<\/b>W\u00a0<\/b>RS<\/b><\/sub>\u00a0= E\u00a0<\/b>pR<\/b><\/sub>\u00a0\u00a0\u2013 E\u00a0<\/b>pS<\/b><\/sub>\u00a0\u00a0 E\u00a0<\/b>pR<\/b><\/sub>\u00a0= qV\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0 E\u00a0<\/b>pS<\/b><\/sub>\u00a0= qV\u00a0<\/b>S<\/b><\/sub>\u00a0\u00a0 W\u00a0<\/b>RS<\/b><\/sub>\u00a0= qV\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 qV\u00a0<\/b>S<\/b><\/sub>\u00a0W\u00a0<\/b>RS<\/b><\/sub>\u00a0= q(V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>S<\/b><\/sub>\u00a0) or W\u00a0<\/b>RS<\/b><\/sub>\u00a0= qU\u00a0<\/b>RS,<\/b><\/sub>\u00a0\u00a0where\u00a0<\/b><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b>\"\"<\/b><\/b><\/b><\/b><\/b>\u00a0<\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

URS\u00a0<\/span><\/b>= V\u00a0<\/b>R\u00a0<\/b><\/sub><\/span>\u2013<\/span><\/b><\/sub>\u00a0\u00a0V\u00a0<\/b>S<\/b><\/sub>\u00a0.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/p>\n

Figure II\u00a0<\/span><\/b>uniform electric field\u00a0<\/b>\u00a0 being the\u00a0<\/b>\u00a0conservative\u00a0<\/b>force\u00a0\u00a0<\/b>, the\u00a0<\/b>work\u00a0<\/b>done by it is\u00a0<\/b>provided by the variation of electric potential energy (initial minus final)\u00a0<\/b>\u00a0 W\u00a0<\/b>RS<\/b><\/sub>\u00a0= E\u00a0<\/b>pR<\/b><\/sub>\u00a0\u00a0\u2013 E\u00a0<\/b>pS<\/b><\/sub>\u00a0\u00a0 E\u00a0<\/b>pR<\/b><\/sub>\u00a0q.V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0 E\u00a0<\/b>p<\/b><\/sub>\u00a0q.V\u00a0<\/b>S<\/b><\/sub>\u00a0\u00a0 W\u00a0<\/b>RS<\/b><\/sub>\u00a0= qV\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 qV\u00a0<\/b>S<\/b><\/sub>\u00a0W\u00a0<\/b>RS<\/b><\/sub>\u00a0= q(V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>S<\/b><\/sub>\u00a0) or W\u00a0<\/b>RS<\/b><\/sub>\u00a0= qU\u00a0<\/b>RS<\/b><\/sub>\u00a0\u00a0 where\u00a0\u00a0<\/b>U\u00a0<\/b>RS<\/b><\/sub>\u00a0=\u00a0<\/b>V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>S<\/b><\/sub>\u00a0.<\/b><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b>\"\"<\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0<\/b>\u00a0<\/b><\/p>\n

But, the\u00a0<\/span><\/b>work of the electric force is also provided by\u00a0<\/span><\/b>W\u00a0<\/b>RS<\/b><\/sub>\u00a0= F.RS.cos\u03b8\u00a0<\/b>= F.RS.d\/RS\u00a0\u00a0<\/b>W\u00a0<\/b>RS<\/b><\/sub>\u00a0=\u00a0<\/b>Fd\u00a0<\/b>\u00a0 E=F\/q\u00a0\u00a0<\/b>F = qE\u00a0<\/b>\u00a0 W\u00a0<\/b>RS<\/b><\/sub>\u00a0= qEd\u00a0\u00a0<\/b>\u00a0 q(V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>S<\/b><\/sub>\u00a0) = qEd\u00a0\u00a0<\/b>(V\u00a0<\/b>R<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>S<\/b><\/sub>\u00a0) = Ed\u00a0\u00a0<\/b>or\u00a0<\/b><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b>\"\"<\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

URS\u00a0<\/span><\/b>=<\/span><\/b><\/sub>\u00a0Ed\u00a0<\/span><\/b>.<\/span><\/b><\/p>\n

Look carefully at the form below with the expressions for the work W and the potential difference U of a variable electric field and a uniform electric field.<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0Observe in\u00a0<\/span><\/b>figures I and II,\u00a0<\/span><\/b>where the\u00a0<\/span><\/b>curves represent the equipotential surfaces\u00a0<\/span><\/b>, the\u00a0<\/span><\/b>red lines the field lines (of force)\u00a0<\/span><\/b>generated\u00a0<\/b>by a\u00a0<\/b>positive source charge Q\u00a0<\/b>and\u00a0<\/b>q, a test charge moving inside this field, in\u00a0<\/b>which:<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Positive electric charges (q)\u00a0<\/span><\/b>move\u00a0<\/span><\/b>spontaneously (W > 0) towards lower potentials.<\/span><\/b><\/p>\n

Negative electric charges (-q)\u00a0<\/span><\/b>move\u00a0<\/span><\/b>spontaneously (W > 0) towards higher potentials.<\/span><\/b><\/p>\n

The\u00a0<\/span><\/b>direction\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>electric field\u00a0<\/span><\/b>is\u00a0<\/span><\/b>always\u00a0<\/span><\/b>from the\u00a0<\/span><\/b>highest to the lowest potential.<\/span><\/b><\/p>\n

The\u00a0<\/span><\/b>three observations above are\u00a0<\/span><\/b>also\u00a0<\/span><\/b>valid\u00a0<\/span><\/b>if the\u00a0<\/span><\/b>electric field is uniform\u00a0<\/span><\/b>as you can see in the\u00a0<\/span><\/b>figure below,<\/span><\/b><\/p>\n

\"\"<\/p>\n

where\u00a0<\/span><\/b>inside the uniform electric field\u00a0<\/span><\/b>created by the\u00a0<\/span><\/b>electrified plates A and B,\u00a0<\/span><\/b>with\u00a0<\/span><\/b>potentials V\u00a0<\/span><\/b>A<\/span><\/b><\/sub>\u00a0\u00a0and\u00a0<\/span><\/b>V\u00a0<\/b>B<\/b><\/sub>\u00a0(V\u00a0<\/b>A<\/b><\/sub>\u00a0> V\u00a0<\/b>B<\/b><\/sub>\u00a0)\u00a0<\/b>there is a solution of NaCl in water with\u00a0<\/b>negative ions moving in the direction of the positive plate and positive ions in the direction of the negative plate.<\/b><\/span>\u00a0<\/b><\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Units of the electric field\u00a0<\/span><\/b>\u00a0 from the expression\u00a0<\/b>E=F\/q,\u00a0<\/b>the field has\u00a0<\/b>SI units\u00a0<\/b>newton\/Coulomb = N\/C\u00a0<\/b>another unit \u00a0\u00a0<\/b>from the expression\u00a0<\/b>U=Ed\u00a0<\/b>, the electric field has\u00a0<\/b>SI units\u00a0<\/b>volt\/meter (V\/m).<\/b><\/span>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/p>\n

Electron-volt (eV)\u00a0<\/span><\/b>\u00a0 corresponds to the\u00a0<\/b>work done when 1 electron left from\u00a0<\/b>rest at point A in an electric field moves spontaneously to point B, so that V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>B<\/b><\/sub>\u00a0= 1V\u00a0\u00a0<\/b>W\u00a0<\/b>AB<\/b><\/sub>\u00a0= q(V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>B<\/b><\/sub>\u00a0)\u00a0<\/b>= 1.6.10\u00a0<\/b>-19<\/b><\/sup>\u00a0.1\u00a0\u00a0<\/b>1 eV=1.6.10\u00a0<\/b>-19<\/b><\/sup>\u00a0J.<\/b><\/span>\u00a0\u00a0\"\"<\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/p>\n

By the expression\u00a0<\/span><\/b>W\u00a0<\/span><\/b>AB<\/span><\/b><\/sub>\u00a0= q(V\u00a0<\/span><\/b>A<\/span><\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/span><\/b>B<\/span><\/b><\/sub>\u00a0),\u00a0<\/span><\/b>if\u00a0<\/span><\/b>points A and B are on the same\u00a0<\/span><\/b>equipotential surface (V\u00a0<\/b>A<\/b><\/sub>\u00a0= V\u00a0<\/b>B<\/b><\/sub>\u00a0= V),\u00a0<\/b>the\u00a0<\/b>work of the electric force in this displacement will be zero\u00a0<\/b>since\u00a0<\/b>W\u00a0<\/b>AB<\/b><\/sub>\u00a0= q.(V \u2013 V) = q.0 = 0.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

 <\/p>\n

What you should know, information and tips<\/span><\/b><\/p>\n

Equipotential surfaces and lines of force of a point charge Q<\/span><\/b><\/p>\n

In the\u00a0<\/span><\/b>particular case of the field of a point charge Q\u00a0<\/span><\/b>,\u00a0<\/span><\/b>symmetry\u00a0<\/span><\/b>suggests that the\u00a0<\/span><\/b>equipotential surfaces\u00a0<\/span><\/b>are\u00a0<\/span><\/b>spherical surfaces concentric\u00a0<\/span><\/b>with the\u00a0<\/span><\/b>charge Q\u00a0<\/span><\/b>and the\u00a0<\/span><\/b>(field) lines of force are radial with the center of the charge.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Note in the\u00a0<\/span><\/b>figures above\u00a0<\/span><\/b>that the\u00a0<\/span><\/b>lines of force (field)\u00a0<\/span><\/b>move\u00a0<\/span><\/b>away\u00a0<\/span><\/b>from the\u00a0<\/span><\/b>positive charges\u00a0<\/span><\/b>and in the\u00a0<\/span><\/b>figures below\u00a0<\/span><\/b>they\u00a0<\/span><\/b>move closer\u00a0<\/span><\/b>to the\u00a0<\/span><\/b>negative ones.<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"\u00a0For\u00a0<\/span><\/b>positive charges, the\u00a0<\/span><\/b>potential of each surface\u00a0<\/span><\/b>increases\u00a0<\/b>as it\u00a0<\/b>approaches the charge\u00a0<\/b>and for\u00a0<\/b>negative charges it decreases as it moves away from the charge.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

The figures below represent several configurations with their respective lines of force and equipotential surfaces.<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

\"\"\u00a0\u00a0Units of the electric field\u00a0<\/span><\/b>\u00a0 from the expression\u00a0<\/b>E=F\/q,\u00a0<\/b>the field has\u00a0<\/b>SI units\u00a0<\/b>newton\/Coulomb = N\/C\u00a0<\/b>another unit \u00a0\u00a0<\/b>from the expression\u00a0<\/b>U=Ed\u00a0<\/b>, the electric field has\u00a0<\/b>SI units\u00a0<\/b>volt\/meter (V\/m).<\/b><\/span>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"\"\"<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/p>\n

\"\"\u00a0\u00a0Electron-volt (eV)\u00a0<\/span><\/b>\u00a0 corresponds to the\u00a0<\/b>work done when 1 electron left from\u00a0<\/b>rest at point A in an electric field moves spontaneously to point B, so that V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>B<\/b><\/sub>\u00a0= 1V\u00a0\u00a0<\/b>W\u00a0<\/b>AB<\/b><\/sub>\u00a0= q(V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>B<\/b><\/sub>\u00a0)\u00a0<\/b>= 1.6.10\u00a0<\/b>-19<\/b><\/sup>\u00a0.1\u00a0\u00a0<\/b>1 eV=1.6.10\u00a0<\/b>-19<\/b><\/sup>\u00a0J.<\/b><\/span>\u00a0\u00a0\"\"<\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/p>\n

\"\"\u00a0\u00a0By the expression\u00a0<\/span><\/b>W\u00a0<\/span><\/b>AB<\/span><\/b><\/sub>\u00a0= q(V\u00a0<\/span><\/b>A<\/span><\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/span><\/b>B<\/span><\/b><\/sub>\u00a0),\u00a0<\/span><\/b>if\u00a0<\/span><\/b>points A and B are on the same\u00a0<\/span><\/b>equipotential surface (V\u00a0<\/b>A<\/b><\/sub>\u00a0= V\u00a0<\/b>B<\/b><\/sub>\u00a0= V),\u00a0<\/b>the\u00a0<\/b>work of the electric force in this displacement will be zero\u00a0<\/b>since\u00a0<\/b>W\u00a0<\/b>AB<\/b><\/sub>\u00a0= q.(V \u2013 V) = q.0 = 0.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Check out the exercises with commented solutions<\/span><\/a><\/h3>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

EQUIPOTENTIAL SURFACES \u2013 WORK OF THE ELECTROSTATIC FORCE Equipotential Surfaces \u2013 Work of the Electrostatic Force The equipotential surface of an electric field\u00a0is defined\u00a0as\u00a0any surface at whose points the\u00a0electric potential is constant. These surfaces have two important properties: \u00a0The\u00a0electric force during the displacement of a point electric charge over an equipotential surface is zero. Equipotential surfaces\u00a0are perpendicular to the lines<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-11444","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=11444"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11444\/revisions"}],"predecessor-version":[{"id":12122,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11444\/revisions\/12122"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=11444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}