{"id":259160,"date":"2022-09-10T12:11:38","date_gmt":"2022-09-10T06:41:38","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/four-charges-equal-to-q-are-placed-at-the-four-corners-of-a-square-and-a-charge-q-is-at-its-centre-if-the-system-is-in-equilibrium-the-value-of-q-is-3\/"},"modified":"2022-09-10T12:11:38","modified_gmt":"2022-09-10T06:41:38","slug":"four-charges-equal-to-q-are-placed-at-the-four-corners-of-a-square-and-a-charge-q-is-at-its-centre-if-the-system-is-in-equilibrium-the-value-of-q-is-3","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/four-charges-equal-to--q-are-placed-at-the-four-corners-of\/","title":{"rendered":"Four charges equal to \u2013 Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Four charges equal to \u2013 Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is","custom_permalink":"question\/physics\/four-charges-equal-to--q-are-placed-at-the-four-corners-of\/"},"categories":[],"acf":{"question":"

Four charges equal to \u2013 Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is<\/p>","options":[{"option":"

-<\/mo>Q<\/mi>4<\/mn><\/mfrac>(<\/mo> <\/mo>1<\/mn>+<\/mo>2<\/mn>2<\/mn><\/msqrt> <\/mo>)<\/mo><\/math><\/p>","correct":false},{"option":"

Q<\/mi>4<\/mn><\/mfrac>(<\/mo> <\/mo>1<\/mn>+<\/mo>2<\/mn>2<\/mn><\/msqrt> <\/mo>)<\/mo><\/math><\/p>","correct":true},{"option":"

-<\/mo>Q<\/mi>2<\/mn><\/mfrac>(<\/mo> <\/mo>1<\/mn>+<\/mo>2<\/mn>2<\/mn><\/msqrt> <\/mo>)<\/mo><\/math><\/p>","correct":false},{"option":"

Q<\/mi>2<\/mn><\/mfrac>(<\/mo> <\/mo>1<\/mn>+<\/mo>2<\/mn>2<\/mn><\/msqrt> <\/mo>)<\/mo><\/math><\/p>","correct":false}],"solution":"

 <\/p>

<\/figure>

Force on any corner charge
F<\/mi>1<\/mn><\/msub>=<\/mo>k<\/mi>Q<\/mi><\/mrow>a<\/mi>2<\/mn><\/msup><\/mfrac>,<\/mo> <\/mo>F<\/mi>2<\/mn><\/msub>=<\/mo>k<\/mi>Q<\/mi>2<\/mn><\/msup><\/mrow>a<\/mi>2<\/mn><\/msup><\/mfrac>,<\/mo> <\/mo>F<\/mi>3<\/mn><\/msub>=<\/mo>k<\/mi>Q<\/mi>2<\/mn><\/msup><\/mrow>(<\/mo>2<\/mn><\/msqrt>a<\/mi>)<\/mo><\/mrow>2<\/mn><\/msup><\/mfrac><\/math><\/p>

F<\/mi>1<\/mn><\/msub>\u2192<\/mo><\/mover>+<\/mo>F<\/mi>2<\/mn><\/msub>\u2192<\/mo><\/mover>+<\/mo>F<\/mi>3<\/mn><\/msub>\u2192<\/mo><\/mover>=<\/mo>F<\/mi>\u2192<\/mo><\/mover><\/math> at equilibrium
Q<\/mi>2<\/mn><\/msup>2<\/mn>a<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>+<\/mo>2<\/mn><\/msqrt>Q<\/mi>2<\/mn><\/msup><\/mrow>a<\/mi>2<\/mn><\/msup><\/mfrac>=<\/mo>Q<\/mi>q<\/mi><\/mrow>a<\/mi>\/<\/mo>2<\/mn><\/msqrt><\/mrow><\/mfenced>2<\/mn><\/msup><\/mfrac><\/math><\/p>

q<\/mi>=<\/mo>Q<\/mi>4<\/mn><\/mfrac>1<\/mn>+<\/mo>2<\/mn>2<\/mn><\/msqrt><\/mrow><\/mfenced><\/math><\/p>","subject":""},"yoast_head":"\nFour charges equal to \u2013 Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Four charges equal to \u2013 Q are placed at the four corners of a square and a charge q is at its centre. 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