To solve this problem, we’ll need to understand the context of the magnetic field. I\u2019ll assume that the magnetic field at point P is due to a current-carrying conductor, with a certain configuration (like a circular loop, for example), and that aaa and bbb represent the distances or radii in the setup.<\/p>\n\n\n\n
Let’s say the magnetic field at point P is created by a current III passing through a circular loop. If a=Ra = Ra=R and b=2Rb = 2Rb=2R, and point P lies at some position in relation to the loop, we would use the Biot-Savart law or Ampere’s Law depending on the exact configuration.<\/p>\n\n\n\n
Explanation using Ampere’s Law for a Circular Loop:<\/h3>\n\n\n\n
For a current-carrying wire in the shape of a circle, the magnetic field at a point on the axis of the loop can be calculated using Ampere’s Law. The formula for the magnetic field at a distance xxx from the center of a circular current loop along its axis is given by:B=\u03bc0IR22(R2+x2)3\/2B = \\frac{\\mu_0 I R^2}{2 (R^2 + x^2)^{3\/2}}B=2(R2+x2)3\/2\u03bc0\u200bIR2\u200b<\/p>\n\n\n\n
Where:<\/p>\n\n\n\n
- \n
- BBB is the magnetic field at point P.<\/li>\n\n\n\n
- \u03bc0\\mu_0\u03bc0\u200b is the permeability of free space (4\u03c0\u00d710\u22127\u2009T\\cdotpm\/A4\\pi \\times 10^{-7} \\, \\text{T\u00b7m\/A}4\u03c0\u00d710\u22127T\\cdotpm\/A).<\/li>\n\n\n\n
- III is the current through the loop.<\/li>\n\n\n\n
- RRR is the radius of the loop.<\/li>\n\n\n\n
- xxx is the distance from the center of the loop along the axis (where point P is located).<\/li>\n<\/ul>\n\n\n\n
Case 1: a=Ra = Ra=R<\/h3>\n\n\n\n
If a=Ra = Ra=R, point P is at a distance equal to the radius of the loop. Plugging this into the formula:B=\u03bc0IR22(R2+R2)3\/2=\u03bc0IR22(2R2)3\/2=\u03bc0I42RB = \\frac{\\mu_0 I R^2}{2 (R^2 + R^2)^{3\/2}} = \\frac{\\mu_0 I R^2}{2 (2R^2)^{3\/2}} = \\frac{\\mu_0 I}{4 \\sqrt{2} R}B=2(R2+R2)3\/2\u03bc0\u200bIR2\u200b=2(2R2)3\/2\u03bc0\u200bIR2\u200b=42\u200bR\u03bc0\u200bI\u200b<\/p>\n\n\n\n
This gives the magnetic field at the point P when a=Ra = Ra=R.<\/p>\n\n\n\n
Case 2: b=2Rb = 2Rb=2R<\/h3>\n\n\n\n
For b=2Rb = 2Rb=2R, point P is at a distance of 2R2R2R along the axis of the loop. Using the formula again:B=\u03bc0IR22(R2+(2R)2)3\/2=\u03bc0IR22(5R2)3\/2=\u03bc0I105RB = \\frac{\\mu_0 I R^2}{2 (R^2 + (2R)^2)^{3\/2}} = \\frac{\\mu_0 I R^2}{2 (5R^2)^{3\/2}} = \\frac{\\mu_0 I}{10 \\sqrt{5} R}B=2(R2+(2R)2)3\/2\u03bc0\u200bIR2\u200b=2(5R2)3\/2\u03bc0\u200bIR2\u200b=105\u200bR\u03bc0\u200bI\u200b<\/p>\n\n\n\n
This gives the magnetic field at point P when b=2Rb = 2Rb=2R.<\/p>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
The magnetic field strength at point P will depend on the specific distance from the loop. By comparing the two cases, the field at a=Ra = Ra=R is stronger than at b=2Rb = 2Rb=2R. The closer the point is to the center of the loop (i.e., smaller RRR), the stronger the magnetic field.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-138.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"QUESTION 5 What is the magnitude of the magnetic field at point P if a = R and b = 2R? The Correct Answer and Explanation is: To solve this problem, we’ll need to understand the context of the magnetic field. I\u2019ll assume that the magnetic field at point P is due to a current-carrying […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-248021","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=248021"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248021\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}