{"id":259114,"date":"2022-09-10T12:11:05","date_gmt":"2022-09-10T06:41:05","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-long-solenoid-of-diameter-0-1-m-has-2x104-turns-per-meter-at-the-centre-of-the-solenoid-a-coil-of-100-turns-and-radius-0-01-m-is-placed-with-its-axis-coinciding-with-the-solenoid\/"},"modified":"2022-09-10T12:11:05","modified_gmt":"2022-09-10T06:41:05","slug":"a-long-solenoid-of-diameter-0-1-m-has-2x104-turns-per-meter-at-the-centre-of-the-solenoid-a-coil-of-100-turns-and-radius-0-01-m-is-placed-with-its-axis-coinciding-with-the-solenoid","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-long-solenoid-of-diameter-01-m-has-2104-turns-per-mete\/","title":{"rendered":"A long solenoid of diameter 0.1 m has \u00a02\u00d7104\u00a0 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is\u00a010\u03c02\u03a9, the total charge flowing through the coil during this time is\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A long solenoid of diameter 0.1 m has \u00a02\u00d7104\u00a0 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is\u00a010\u03c02\u03a9, the total charge flowing through the coil during this time is\u00a0","custom_permalink":"question\/physics\/a-long-solenoid-of-diameter-01-m-has-2104-turns-per-mete\/"},"categories":[],"acf":{"question":"

A long solenoid of diameter 0.1 m has  2<\/mn>\u00d7<\/mo>10<\/mn>4<\/mn><\/msup><\/mrow><\/mstyle><\/math>  turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10\u03c0<\/mtext>2<\/mn><\/msup>\u03a9<\/mi><\/mrow><\/mstyle><\/math>, the total charge flowing through the coil during this time is <\/p>","options":[{"option":"

16<\/mn>\u03bcC<\/mi><\/mstyle><\/math> <\/p>","correct":false},{"option":"

32<\/mn>\u03bcC<\/mi><\/mstyle><\/math> <\/p>","correct":true},{"option":"

16<\/mn>\u03c0\u03bcC<\/mi><\/mrow><\/mstyle><\/math><\/p>","correct":false},{"option":"

32<\/mn>\u03c0\u03bcC<\/mi><\/mrow><\/mstyle><\/math><\/p>","correct":false}],"solution":"

 Given <\/mtext>n<\/mi>=<\/mo>2<\/mn>\u00d7<\/mo>10<\/mn>4<\/mn><\/msup>;<\/mo>I<\/mi>=<\/mo>4<\/mn> <\/mo>A<\/mi><\/mrow><\/mstyle><\/math><\/p>

Initially I = 0 A<\/p>

\u2234<\/mo>B<\/mi>i<\/mi><\/msub>=<\/mo>0<\/mn> or <\/mtext>\u03d5<\/mi>i<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow><\/mstyle><\/math><\/p>

Finally, the magnetic field at the centre of the solenoid is given as<\/p>

B<\/mi>f<\/mi><\/msub>=<\/mo>\u03bc<\/mi>o<\/mi><\/msub>nI<\/mi><\/mtd><\/mtr>B<\/mi>f<\/mi><\/msub>=<\/mo>4<\/mn>\u03c0<\/mi>\u00d7<\/mo>10<\/mn>-<\/mo>7<\/mn><\/mrow><\/msup>\u00d7<\/mo>2<\/mn>\u00d7<\/mo>10<\/mn>4<\/mn><\/msup>\u00d7<\/mo>4<\/mn><\/mtd><\/mtr>B<\/mi>f<\/mi><\/msub>=<\/mo>32<\/mn>\u03c0<\/mi>\u00d7<\/mo>10<\/mn>-<\/mo>3<\/mn><\/mrow><\/msup> <\/mo>T<\/mi><\/mtd><\/mtr><\/mtable><\/mstyle><\/math><\/p>

Final magnetic flux through the coil is given as <\/p>

\u03d5<\/mi>f<\/mi><\/msub>=<\/mo>nBA<\/mi> <\/mspace> <\/mo> <\/mo> <\/mo> <\/mo>=<\/mo>100<\/mn>\u00d7<\/mo>32<\/mn>\u03c0<\/mi>\u00d7<\/mo>10<\/mn>-<\/mo>3<\/mn><\/mrow><\/msup>\u00d7<\/mo>\u03c0<\/mi>\u00d7<\/mo>(<\/mo>0<\/mn>.<\/mo>01<\/mn>)<\/mo>2<\/mn><\/msup> <\/mspace>\u03d5<\/mi>f<\/mi><\/msub>=<\/mo>32<\/mn>\u03c0<\/mi>2<\/mn><\/msup>\u00d7<\/mo>10<\/mn>-<\/mo>5<\/mn><\/mrow><\/msup>Tm<\/mi>2<\/mn><\/msup><\/mrow><\/mstyle><\/math><\/p>

Induced charge,<\/p>

q<\/mi>=<\/mo>|<\/mo>\u0394<\/mi>\u03d5<\/mi>|<\/mo><\/mrow>R<\/mi><\/mfrac>=<\/mo>\u03d5<\/mi>f<\/mi><\/msub>-<\/mo>\u03d5<\/mi>i<\/mi><\/msub><\/mrow><\/mfenced>R<\/mi><\/mfrac>=<\/mo>32<\/mn>\u03c0<\/mi>2<\/mn><\/msup>\u00d7<\/mo>10<\/mn>-<\/mo>5<\/mn><\/mrow><\/msup><\/mrow>10<\/mn>\u03c0<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>=<\/mo>32<\/mn>\u00d7<\/mo>10<\/mn>-<\/mo>6<\/mn><\/mrow><\/msup>C<\/mi>=<\/mo>32<\/mn>\u03bc<\/mi>C<\/mi><\/mrow><\/mstyle><\/math><\/p>","subject":""},"yoast_head":"\nA long solenoid of diameter 0.1 m has \u00a02\u00d7104\u00a0 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. 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