{"id":239506,"date":"2022-09-10T07:09:04","date_gmt":"2022-09-10T01:39:04","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/two-point-charges-placed-at-a-certain-distance-r-in-air-exert-a-force-f-on-each-other-then-the-distance-r-at-which-these-charges-will-exert-the-same-force-in-a-medium-of-dielectric-constant-k-is-g\/"},"modified":"2025-06-26T17:48:53","modified_gmt":"2025-06-26T12:18:53","slug":"two-point-charges-placed-at-a-certain-distance-r-in-air-exert-a-force-f-on-each-other-then-the-distance-r-at-which-these-charges-will-exert-the-same-force-in-a-medium-of-dielectric-constant-k-is-g","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/two-point-charges-placed-at-a-certain-distance-r-in-air-exer\/","title":{"rendered":"Two point charges placed at a certain distance r in air exert a force F on each other. Then, the distance r&#8217; at which these charges will exert the same force in a medium of dielectric constant K is given by\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Two point charges placed at a certain distance r in air exert a force F on each other. Then, the distance r' at which these charges will exert the same force in a medium of dielectric constant K is given by\u00a0","custom_permalink":"question\/physics\/two-point-charges-placed-at-a-certain-distance-r-in-air-exer\/"},"categories":[],"acf":{"question":"<p>Two point charges placed at a certain distance r in air exert a force F on each other. Then, the distance r' at which these charges will exert the same force in a medium of dielectric constant K is given by&nbsp;<\/p>","options":[{"option":"<p>r<\/p>","correct":false},{"option":"<p>r\/K<\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">r<\/mi><mo>\/<\/mo><msqrt><mi mathvariant=\"normal\">K<\/mi><\/msqrt><\/math><\/p>","correct":true},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">r<\/mi><msqrt><mi mathvariant=\"normal\">K<\/mi><\/msqrt><\/math><\/p>","correct":false}],"solution":"<p>Force exerted between two point charges in air&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">F<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">q<\/mi><mn>1<\/mn><\/msub><msub><mi mathvariant=\"normal\">q<\/mi><mn>2<\/mn><\/msub><\/mrow><mrow><mn>4<\/mn><msub><mi>\u03c0\u03b5<\/mi><mn>0<\/mn><\/msub><msup><mi mathvariant=\"normal\">r<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><\/math><br>So, force exerted between two point charges in a medium of <strong>dielectric constant<\/strong>\r\n&nbsp;<br>K is&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi mathvariant=\"normal\">F<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">q<\/mi><mn>1<\/mn><\/msub><msub><mi mathvariant=\"normal\">q<\/mi><mn>2<\/mn><\/msub><\/mrow><mrow><mn>4<\/mn><msub><mi>\u03c0\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">K<\/mi><msup><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><\/mrow><\/mfenced><mn>2<\/mn><\/msup><\/mrow><\/mfrac><\/math><br>Where, &nbsp;r' is the distance.<br>Given, F = F'<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">q<\/mi><mn>1<\/mn><\/msub><msub><mi mathvariant=\"normal\">q<\/mi><mn>2<\/mn><\/msub><\/mrow><mrow><mn>4<\/mn><msub><mi>\u03c0\u03b5<\/mi><mn>0<\/mn><\/msub><msup><mi mathvariant=\"normal\">r<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">q<\/mi><mn>1<\/mn><\/msub><msub><mi mathvariant=\"normal\">q<\/mi><mn>2<\/mn><\/msub><\/mrow><mrow><mn>4<\/mn><msub><mi>\u03c0\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">K<\/mi><msup><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><\/mrow><\/mfenced><mn>2<\/mn><\/msup><\/mrow><\/mfrac><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mn>1<\/mn><msup><mi mathvariant=\"normal\">r<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mi mathvariant=\"normal\">K<\/mi><msup><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><\/mrow><\/mfenced><mn>2<\/mn><\/msup><\/mrow><\/mfrac><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><msup><mi mathvariant=\"normal\">r<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mi mathvariant=\"normal\">K<\/mi><msup><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><\/mrow><\/mfenced><mn>2<\/mn><\/msup><mo stretchy=\"false\">\u21d2<\/mo><mi mathvariant=\"normal\">r<\/mi><mo>=<\/mo><msqrt><mi mathvariant=\"normal\">K<\/mi><\/msqrt><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><\/mtd><\/mtr><mtr><mtd><mo>\u2234<\/mo><mi mathvariant=\"normal\">r<\/mi><mo>'<\/mo><mo>=<\/mo><mfrac><mi mathvariant=\"normal\">r<\/mi><msqrt><mi mathvariant=\"normal\">K<\/mi><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Two point charges placed at a certain distance r in air exert a force F on each other. 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