{"id":11382,"date":"2024-11-11T13:39:08","date_gmt":"2024-11-11T13:39:08","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11382"},"modified":"2024-12-03T14:09:46","modified_gmt":"2024-12-03T14:09:46","slug":"forca-magnetica-sobre-uma-carga-movel-imersa-num-campo-magnetico-2","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletromagnetismo\/forca-magnetica-sobre-uma-carga-movel-imersa-num-campo-magnetico-2\/","title":{"rendered":"Magnetic force on a moving charge immersed in a magnetic field"},"content":{"rendered":"

MAGNETIC FORCE ON A MOVING CHARGE IMMERSED IN A MAGNETIC FIELD<\/span><\/h1>\n
\n

Magnetic force on a moving charge immersed in a magnetic field<\/span><\/b><\/p>\n

\u00a0When an\u00a0<\/span><\/b>electric charge\u00a0<\/span><\/b>moves\u00a0<\/span><\/b>at high speed\u00a0\u00a0<\/span>\"\"<\/b>\u00a0within\u00a0<\/span><\/b>a magnetic field\u00a0<\/span>\"\"<\/b>\u00a0<\/b><\/p>\n

A force of magnetic origin\u00a0\u00a0<\/span>\"\"\u00a0(\u00a0<\/span><\/b>called the Lorentz force) arises over it,\u00a0<\/span><\/b>with the following characteristics:<\/span><\/b><\/p>\n

\"\"\u00a0Direction and sense\u00a0\u00a0<\/span>\"\"\u00a0\"\"provided by the left hand rule\u00a0<\/span><\/b>as shown in<\/span><\/b><\/p>\n

\"\"<\/p>\n

figure above.<\/span><\/b><\/p>\n

Note in the\u00a0<\/span><\/b>figure on the right that\u00a0\u00a0<\/span>\"\"\u00a0is perpendicular to\u00a0\u00a0<\/span>\"\"\u00a0and to\u00a0\u00a0<\/span>\"\",\u00a0<\/span><\/b>which\u00a0<\/span><\/b>imposes the condition that\u00a0\u00a0<\/span>\"\"and\u00a0<\/span>\"\"\u00a0<\/b>must\u00a0<\/span><\/b>belong to the\u00a0<\/span><\/b>same plane.<\/b><\/span><\/b><\/b><\/b><\/p>\n

Also note that\u00a0<\/span><\/b>\u03b8 is the angle between\u00a0\u00a0<\/span>\"\"and\u00a0\u00a0<\/span>\"\".<\/span><\/b><\/p>\n

\"\"<\/p>\n

Knowing the direction and sense of\u00a0\u00a0<\/span>\"\"and from\u00a0\u00a0<\/span>\"\"\u00a0<\/b>you can, using the\u00a0<\/span><\/b>left-hand rule,\u00a0<\/span><\/b>determine\u00a0<\/b>the direction and sense of the magnetic force\u00a0\u00a0<\/b>\u00a0as you can see in the\u00a0<\/b>diagram below,\u00a0<\/b>where a\u00a0<\/b>positive charge\u00a0<\/b>moves\u00a0<\/b>with speed\u00a0\u00a0<\/b>\u00a0inside\u00a0<\/b>a\u00a0<\/b>uniform magnetic field.\u00a0<\/b><\/span>\u00a0<\/b>\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Note that the\u00a0<\/span><\/b>direction of the lines of magnetic induction and consequently of\u00a0\u00a0<\/span>\"\"\u00a0is from the\u00a0<\/span><\/b>north pole to the south pole.<\/b><\/span><\/b><\/b><\/b><\/p>\n

By adjusting\u00a0<\/span><\/b>the\u00a0<\/span><\/b>index and middle fingers in the directions of\u00a0\u00a0<\/span>\"\"and from\u00a0\u00a0<\/span>\"\"<\/b>\u00a0you\u00a0<\/span><\/b>determine the direction and sense of\u00a0<\/span>\"\".<\/span><\/b><\/p>\n

Note:\u00a0<\/span><\/b>If\u00a0<\/span><\/b>q is negative you must reverse the direction of the magnetic force\u00a0\u00a0<\/span>\"\".<\/span><\/b><\/p>\n

 <\/p>\n

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

 <\/p>\n

\"\"<\/p>\n

Since the\u00a0<\/span><\/b>magnetic force\u00a0<\/span><\/b>always has a direction perpendicular to\u00a0<\/b>the<\/b><\/sub>\u00a0velocity vector\u00a0<\/b>and since the\u00a0<\/b>power of a force\u00a0<\/b>is provided by\u00a0<\/b>Po\u00a0<\/b>= F\u00a0<\/b>m<\/b><\/sub>\u00a0.V.cos\u03b8,\u00a0<\/b>then \u03b8 = 90\u00a0<\/b>o<\/b><\/sup>\u00a0\u00a0and cos 90\u00a0<\/b>o<\/b><\/sup>\u00a0= 0\u00a0\u00a0<\/b>Po\u00a0<\/b>=<\/b><\/sub>\u00a0F\u00a0<\/b>m<\/b><\/sub>\u00a0.V.0\u00a0\u00a0<\/b>\u00a0 Po\u00a0<\/b>= 0\u00a0<\/b>\u00a0 if the\u00a0<\/b>power<\/b><\/sub>\u00a0is zero the work will also be\u00a0<\/b>, since Po\u00a0<\/b>=<\/b><\/sub>\u00a0W\/\u2206t\u00a0<\/b>0 = W\/\u2206t<\/b><\/span>\u00a0\"\"<\/b><\/b>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b><\/b><\/b><\/b>\"\"<\/b><\/b>\"\"<\/b><\/b><\/b><\/b>\"\"\"\"<\/b><\/p>\n

W = 0.\u00a0<\/span><\/b><\/p>\n

The work done by the magnetic force is always zero or, the magnetic force never does work.<\/span><\/b><\/p>\n

\"\"\u00a0Convention<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Some examples:<\/span><\/b><\/p>\n

The\u00a0<\/span><\/b>figures\u00a0<\/span><\/b>below\u00a0<\/span><\/b>represent\u00a0<\/span><\/b>the\u00a0<\/span><\/b>magnetic forces and the final arrangement of the left hand.\u00a0<\/span><\/b>Note that in\u00a0<\/span><\/b>cases b and c\u00a0<\/span><\/b>the\u00a0<\/span><\/b>magnetic force\u00a0<\/span>\"\"<\/b>has\u00a0<\/span><\/b>the opposite direction\u00a0<\/span><\/b>to that given by the\u00a0<\/span><\/b>left-hand rule, since the electric charge is negative.<\/span><\/b><\/p>\n

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 <\/p>\n

 <\/p>\n

Magnetic force on electric charge \u2013 particular cases<\/span><\/b><\/p>\n

 <\/p>\n

You have already seen that the\u00a0<\/span><\/b>main characteristics of the magnetic force\u00a0<\/span><\/b>that acts on an\u00a0<\/b>electric charge immersed in a magnetic field have the following characteristics:<\/b><\/span>\u00a0\"\"<\/b><\/b><\/p>\n

\"\"\u00a0Direction and sense\u00a0<\/span><\/b>provided by\u00a0<\/b>left hand rule\u00a0<\/b>as\u00a0<\/b>shown in the\u00a0<\/b>figure below.<\/b><\/span>\u00a0\"\"\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Note in the\u00a0<\/span><\/b>figure on the right\u00a0<\/span><\/b>that\u00a0\u00a0<\/span>\"\"\u00a0is\u00a0<\/span><\/b>perpendicular to\u00a0\u00a0<\/span>\"\"\u00a0and to\u00a0\u00a0<\/span>\"\"<\/b>, which imposes the condition that\u00a0\u00a0<\/span>\"\"and\u00a0<\/span>\"\"must belong to the same plane. Also note that \u03b8 is the angle between\u00a0\u00a0<\/span>\"\"and\u00a0\u00a0<\/span>\"\".<\/span><\/b><\/p>\n

\"\"\u00a0Intensity of\u00a0\u00a0<\/span>\"\"\u00a0\"\"<\/b>is\u00a0<\/span><\/b>proportional to q, V, B\u00a0<\/span><\/b>and\u00a0<\/span><\/b>sen\u03b8,\u00a0<\/span><\/b>obeying the equation:<\/span><\/b><\/p>\n

\"\"<\/p>\n

Charge\u00a0<\/span><\/b>at rest (V = 0) or thrown with velocity\u00a0\u00a0<\/span>\"\"parallel to the lines of induction of a uniform magnetic field<\/span>\"\"<\/b><\/p>\n

 <\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Electric charge\u00a0\u00a0<\/span><\/b>q\u00a0<\/span><\/b>\u00a0launched with velocity\u00a0\u00a0<\/span>\"\"perpendicular to the lines of induction of a uniform magnetic field<\/span>\"\"<\/b><\/p>\n

Note that\u00a0<\/span><\/b>in this case\u00a0<\/span><\/b>the angle between\u00a0\u00a0<\/span>\"\"and\u00a0\u00a0<\/span>\"\"is\u00a0<\/span><\/b>90\u00a0<\/span><\/b>\u00b0<\/span><\/b><\/sup>\u00a0\u00a0(they are perpendicular) and that sin90\u00a0<\/span><\/b>\u00b0<\/span><\/b><\/sup>\u00a0= 1.<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

The\u00a0<\/span><\/b>period T\u00a0<\/b>(time that the charge q takes to complete a complete revolution) is\u00a0<\/b>given by\u00a0<\/b>V = \u0394S \/ \u0394t\u00a0<\/b>\u00a0 in a\u00a0<\/b>complete revolution\u00a0<\/b>\u00a0 \u0394S = 2\u03c0R and \u0394t = T\u00a0\u00a0<\/b>V = 2\u03c0R \/ T\u00a0<\/b>(II).<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b>\u00a0\u00a0\"\"\"\"\u00a0<\/b><\/b><\/b><\/p>\n

Substituting\u00a0<\/span><\/b>II\u00a0<\/span><\/b>in\u00a0<\/span><\/b>I\u00a0\u00a0<\/span>\"\"\u00a0 R = m.(2\u03c0R\/T)\/qB\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/b>T = 2\u03c0m\/qB\u00a0\u00a0<\/span><\/b>\u00a0(period of the MCU).<\/span><\/b><\/p>\n

Note that the\u00a0<\/span><\/b>period (T) of the circular motion\u00a0<\/span><\/b>does not depend on the speed\u00a0<\/b>at which the\u00a0<\/b>particle q penetrates the magnetic field nor on the radius of the circumference.<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

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

 <\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Note in the\u00a0<\/span><\/b>expression for the period (T)\u00a0<\/span><\/b>that it\u00a0<\/span><\/b>does not depend on the speed of the particle, nor on the radius of the circle.<\/span><\/b><\/p>\n

The work done by\u00a0<\/span>\"\"\u00a0on q is zero\u00a0<\/span><\/b>, since\u00a0<\/span>\"\"<\/b>\u00a0it is perpendicular to the plane formed by\u00a0<\/span>\"\"e\u00a0<\/span>\"\"<\/b>and\u00a0<\/span><\/b>W =\u00a0<\/span><\/b>F\u00a0<\/b>m<\/b><\/sub>\u00a0.d.cos90\u00a0<\/b>0<\/b><\/sup>\u00a0= F\u00a0<\/b>m<\/b><\/sub>\u00a0.d.0\u00a0<\/b>= 0\u00a0<\/b>.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

\"\"<\/p>\n

Magnetic and electric fields acting on a particle or beam of electrified particles with charge q<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

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

MAGNETIC FORCE ON A MOVING CHARGE IMMERSED IN A MAGNETIC FIELD Magnetic force on a moving charge immersed in a magnetic field \u00a0When an\u00a0electric charge\u00a0moves\u00a0at high speed\u00a0\u00a0\u00a0within\u00a0a magnetic field\u00a0\u00a0 A force of magnetic origin\u00a0\u00a0\u00a0(\u00a0called the Lorentz force) arises over it,\u00a0with the following characteristics: \u00a0Direction and sense\u00a0\u00a0\u00a0provided by the left hand rule\u00a0as shown in figure above. Note in the\u00a0figure on the<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":243,"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-11382","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11382","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=11382"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11382\/revisions"}],"predecessor-version":[{"id":12054,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11382\/revisions\/12054"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/243"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=11382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}