{"id":64485,"date":"2025-05-12T09:47:47","date_gmt":"2025-05-12T06:47:47","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64485"},"modified":"2025-05-12T09:47:47","modified_gmt":"2025-05-12T06:47:47","slug":"solenoid-electromagnetic-force","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/","title":{"rendered":"Solenoid Coil Electromagnetic Force Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 class=\"text-lg font-display font-bold\">Solenoid Magnetic Force Estimator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"64485\" data-favorite-title=\"Solenoid Coil Electromagnetic Force\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/\" data-favorite-excerpt=\"This calculator estimates the electromagnetic force (EMF) produced by a solenoid coil based on the number of turns, current, core material, and solenoid dimensions. It\u2019s ideal for designing actuators, relays, valves, and magnetic lifting devices.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-electrical\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64485\" data-post=\"64485\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Number of turns<\/label><div class=\"term\">N<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"number_of_turns\" id=\"field-1\" min=\"1\" step=\"1\" value=\"100\"\/><small>Total number of turns in the coil<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Current<\/label><div class=\"term\">I<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"current\" id=\"field-2\" min=\"0.01\" step=\"0.01\" value=\"2\"\/><div class=\"unit\">A<\/div><small>Current through the coil<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Core area<\/label><div class=\"term\">A<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"core_area\" id=\"field-3\" min=\"0.01\" step=\"0.01\" value=\"2\"\/><div class=\"unit\">cm\u00b2<\/div><small>Cross-sectional area of core (cm\u00b2)<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Air gap<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"air_gap\" id=\"field-4\" min=\"0.01\" step=\"0.01\" value=\"1\"\/><div class=\"unit\">mm<\/div><small>Gap between core and armature (mm)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64485\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Electromagnetic Force<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"N\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64485\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">1<\/span><span class=\"reaction text-3xl\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<p><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Solenoid Electromagnetic Force Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$F = \\frac{{B^2 \\cdot A}}{{2 \\cdot \\mu_0}}$$\n$$B = \\mu_0 \\cdot \\mu_r \\cdot \\frac{{N \\cdot I}}{L}$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$F$$ = electromagnetic force (N)  <\/li>\n<li>$$B$$ = magnetic flux density (T)  <\/li>\n<li>$$A$$ = cross-sectional area of the core (m\u00b2)  <\/li>\n<li>$$N$$ = number of turns  <\/li>\n<li>$$I$$ = current (A)  <\/li>\n<li>$$L$$ = length of coil (m)  <\/li>\n<li>$$\\mu_0$$ = permeability of free space $$\u2248 4\\pi <\/li>\n<\/ul>\n<p>These formulas assume a uniform magnetic field and cylindrical geometry.<br \/>\r\n<\/section><br \/>\n<section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Solenoid Coil Electromagnetic Force \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<p>\n<strong>Given:<\/strong><\/p>\n<ul>\n<li>$$N$$ = 1000 turns  <\/li>\n<li>$$I$$ = 2 A  <\/li>\n<li>$$L$$ = 0.1 m  <\/li>\n<li>$$A$$ = 0.0002 m\u00b2  <\/li>\n<li>$$\\mu_r$$ = 1000<\/li>\n<\/ul>\n<p><strong>Calculation:<\/strong><\/p>\n<ol>\n<li>$$B = 4\\pi \\cdot 10^{-7} \\cdot 1000 \\cdot \\frac{1000 \\cdot 2}{0.1} \u2248 0.0251~\\text{T}$$<\/li>\n<li>$$F = \\frac{(0.0251)^2 \\cdot 0.0002}{2 \\cdot 4\\pi \\cdot 10^{-7}} \u2248 \\frac{1.26 \\cdot 10^{-7}}{2.513 \\cdot 10^{-6}} \u2248 0.0501~\\text{N}$$<\/li>\n<\/ol>\n<p>\n\r\n<\/section><br \/>\nSolenoid coils are used in countless electromagnetic devices to convert electrical energy into mechanical motion. This calculator helps engineers and students predict the magnetic pulling force generated by a solenoid under certain current and geometric conditions. It\u2019s particularly useful in applications involving magnetic actuators, electromagnetic locks, and robotic grippers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator estimates the electromagnetic force (EMF) produced by a solenoid coil based on the number of turns, current, core material, and solenoid dimensions. It\u2019s ideal for designing actuators, relays, valves, and magnetic lifting devices.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[21],"class_list":["post-64485","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-electrical"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64485"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485\/revisions"}],"predecessor-version":[{"id":64487,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485\/revisions\/64487"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}