{"id":257771,"date":"2022-09-10T11:55:12","date_gmt":"2022-09-10T06:25:12","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the-origin-under-the-action-of-an-electric-field-e%e2%86%922e0i-and-b%e2%86%92b0i-with\/"},"modified":"2022-09-10T11:55:12","modified_gmt":"2022-09-10T06:25:12","slug":"a-particle-of-charge-q-and-mass-m-starts-moving-from-the-origin-under-the-action-of-an-electric-field-e%e2%86%922e0i-and-b%e2%86%92b0i-with","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/","title":{"rendered":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.","custom_permalink":"question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/"},"categories":[],"acf":{"question":"<p>A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover accent=\"true\"><mi>E<\/mi><mo>\u2192<\/mo><\/mover><mo>=<\/mo><mrow><mn>2<\/mn><msub><mi>E<\/mi><mn>0<\/mn><\/msub><\/mrow><mover accent=\"true\"><mi>i<\/mi><mo>^<\/mo><\/mover><\/math>&nbsp;and&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover><mi>B<\/mi><mo>\u2192<\/mo><\/mover><mo>=<\/mo><msub><mi>B<\/mi><mn>0<\/mn><\/msub><mover accent=\"true\"><mi>i<\/mi><mo>^<\/mo><\/mover><\/math>&nbsp;with a velocity&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover><mi>v<\/mi><mo>\u2192<\/mo><\/mover><mo>=<\/mo><msub><mi>v<\/mi><mn>0<\/mn><\/msub><mover accent=\"true\"><mi>j<\/mi><mo>^<\/mo><\/mover><\/math>&nbsp;. The speed of the particle will becomes&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/math>&nbsp;after a time.<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>t<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>m<\/mi><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mi>q<\/mi><msub><mi>E<\/mi><mi>o<\/mi><\/msub><\/mrow><\/mfrac><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>t<\/mi><mo>=<\/mo><mfrac><mrow><mn>2<\/mn><mi>B<\/mi><mi>q<\/mi><\/mrow><mrow><mi>m<\/mi><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><\/mfrac><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>t<\/mi><mo>=<\/mo><mfrac><mrow><msqrt><mn>3<\/mn><\/msqrt><mi>B<\/mi><mi>q<\/mi><\/mrow><mrow><mi>m<\/mi><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><\/mfrac><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>t<\/mi><mo>=<\/mo><mfrac><mrow><msqrt><mn>3<\/mn><\/msqrt><mi>m<\/mi><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><mi>q<\/mi><msub><mi>E<\/mi><mi>o<\/mi><\/msub><\/mrow><\/mfrac><\/math><\/p>","correct":true}],"solution":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover accent=\"true\"><mi>E<\/mi><mo>\u2192<\/mo><\/mover><\/math>&nbsp;is parallel to&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover accent=\"true\"><mi>B<\/mi><mo>\u2192<\/mo><\/mover><\/math>&nbsp;and&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover accent=\"true\"><mi>V<\/mi><mo>\u2192<\/mo><\/mover><\/math>&nbsp;is perpendicular to both, &nbsp;therefore path of the particle is a helix&nbsp;with&nbsp;increasing pitch .<\/p><p>Speed of particle at any time \u2018t\u2019 is&nbsp;given by<br>&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>V<\/mi><mo>=<\/mo><msqrt><msubsup><mi>V<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>V<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>V<\/mi><mi>z<\/mi><mn>2<\/mn><\/msubsup><\/msqrt><\/math><br>here, &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msubsup><mi>V<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>V<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mo>=<\/mo><msubsup><mi>V<\/mi><mn>0<\/mn><mn>2<\/mn><\/msubsup><\/math>&nbsp; &nbsp;at all times because the yz components will remain same.<\/p><p>Only the x component will increase due to electric field.<br>After some time, it is given that &nbsp;&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>V<\/mi><mo>=<\/mo><mn>2<\/mn><msub><mi>V<\/mi><mi>o<\/mi><\/msub><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>U<\/mi><mi>sin<\/mi><mi>g<\/mi><mo>,<\/mo><mo>&nbsp;<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><mi>V<\/mi><mo>=<\/mo><msqrt><msubsup><mi>V<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>V<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>V<\/mi><mi>z<\/mi><mn>2<\/mn><\/msubsup><\/msqrt><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>\u21d2<\/mo><mn>2<\/mn><msub><mi>V<\/mi><mi>o<\/mi><\/msub><mo>=<\/mo><msqrt><msubsup><mi>V<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msup><msub><mi>V<\/mi><mi>o<\/mi><\/msub><mn>2<\/mn><\/msup><\/msqrt><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>\u21d2<\/mo><msub><mi>V<\/mi><mi>x<\/mi><\/msub><mo>&nbsp;<\/mo><mo>=<\/mo><mo>&nbsp;<\/mo><msqrt><mn>3<\/mn><\/msqrt><msub><mi>V<\/mi><mi>o<\/mi><\/msub><\/math><br>&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>E<\/mi><mi>q<\/mi><mi>u<\/mi><mi>a<\/mi><mi>t<\/mi><mi>i<\/mi><mi>o<\/mi><mi>n<\/mi><mo>&nbsp;<\/mo><mi>o<\/mi><mi>f<\/mi><mo>&nbsp;<\/mo><mi>k<\/mi><mi>i<\/mi><mi>n<\/mi><mi>e<\/mi><mi>m<\/mi><mi>a<\/mi><mi>t<\/mi><mi>i<\/mi><mi>c<\/mi><mi>s<\/mi><mo>,<\/mo><mo>&nbsp;<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><msub><mi>V<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><msub><mi>U<\/mi><mi>x<\/mi><\/msub><mo>+<\/mo><msub><mi>a<\/mi><mi>x<\/mi><\/msub><mi>t<\/mi><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>\u21d2<\/mo><msqrt><mn>3<\/mn><\/msqrt><msub><mi>V<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mfrac><mrow><mi>q<\/mi><mn>2<\/mn><msub><mi>E<\/mi><mi>o<\/mi><\/msub><\/mrow><mi>M<\/mi><\/mfrac><mi>t<\/mi><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u21d2<\/mo><mi>t<\/mi><mo>=<\/mo><mfrac><mrow><msqrt><mn>3<\/mn><\/msqrt><mi>M<\/mi><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><mi>q<\/mi><msub><mi>E<\/mi><mi>o<\/mi><\/msub><\/mrow><\/mfrac><\/math>&nbsp;.<\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time. - Infinity Learn by Sri Chaitanya","description":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/","og_locale":"en_US","og_type":"article","og_title":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time. - Infinity Learn by Sri Chaitanya","og_description":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.","og_url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/","name":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time. - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-09-10T06:25:12+00:00","dateModified":"2022-09-10T06:25:12+00:00","description":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-of-charge-q-and-mass-m-starts-moving-from-the\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"A particle of charge \u2018q\u2019 and mass \u2018m\u2019 starts moving from the origin under the action of an electric field \u00a0E\u2192=2E0i^\u00a0and\u00a0B\u2192=B0i^\u00a0with a velocity\u00a0v\u2192=v0j^\u00a0. The speed of the particle will becomes\u00a02v0\u00a0after a time."}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/257771"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=257771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=257771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}