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Page 1 JEE Solved Example on Electromagnetic Induction and Alternating Current JEE Mains Q1: A conducting loop of radius ?? is present in a uniform magnetic field ?? perpendicular to the plane of the ring. If radius ?? varies as a function of time't', as ?? = ?? ?? + ?? . The e.m.f. induced in the loop is (A) ?? ?? (?? ?? + ?? )?? clockwise (B) ?? (?? ?? + ?? )?? clockwise (C) ?? ?? (?? ?? + ?? )?? anticlockwise (D) zero Ans:(?? )?? = ?? ?? 2 = ?? (?? 0 + ?? ) 2 ???? ???? = 2?? (?? 0 + ?? ) ?? = -?????? ???? = -2???? (?? 0 + ?? ) ? 2?? (?? 0 + ?? )?? is induced anticlockwise. Note: To have clarity about clockwise or anticlockwise, remember as flux increases, it tries to reduce net magnetic field ?? . Hence voltage is induced. It leads to current in direction of voltage, which reduces magnetic field. Q2: A square wire loop of ???? .?? ???? side lies at right angle to a uniform magnetic field of ???? ?? . A 10V light bulb is in a series with the loop as shown in the Figure. The magnetic field is decreasing steadily to zero over a time interval ?? ?? . The bulb will shine full brightness if ?? ?? is equal to Page 2 JEE Solved Example on Electromagnetic Induction and Alternating Current JEE Mains Q1: A conducting loop of radius ?? is present in a uniform magnetic field ?? perpendicular to the plane of the ring. If radius ?? varies as a function of time't', as ?? = ?? ?? + ?? . The e.m.f. induced in the loop is (A) ?? ?? (?? ?? + ?? )?? clockwise (B) ?? (?? ?? + ?? )?? clockwise (C) ?? ?? (?? ?? + ?? )?? anticlockwise (D) zero Ans:(?? )?? = ?? ?? 2 = ?? (?? 0 + ?? ) 2 ???? ???? = 2?? (?? 0 + ?? ) ?? = -?????? ???? = -2???? (?? 0 + ?? ) ? 2?? (?? 0 + ?? )?? is induced anticlockwise. Note: To have clarity about clockwise or anticlockwise, remember as flux increases, it tries to reduce net magnetic field ?? . Hence voltage is induced. It leads to current in direction of voltage, which reduces magnetic field. Q2: A square wire loop of ???? .?? ???? side lies at right angle to a uniform magnetic field of ???? ?? . A 10V light bulb is in a series with the loop as shown in the Figure. The magnetic field is decreasing steadily to zero over a time interval ?? ?? . The bulb will shine full brightness if ?? ?? is equal to (A) 20 ms (B) 0.02 ms (C) 2 ms (D) 0.2 ms Ans:(?? )?? = ???? ??? 10 = 20× (0.1) 2 ??? ? ??? = 20 ms Q3: The dimensions of permeability of free space can be given by (A) [?????? -?? ?? -?? ] (B) [???? ?? -?? ] (C) [???? -?? ?? ?? ?? ?? ] (D) [???? ?? -?? ] Ans : (A) [MA -1 T -2 ] Now ?? = ?? 0 i 2?? (for circular wire) ? [?? 0 ] = [?? ][r] [i] = [MA -1 T -1 ][L] [A] = MLA -2 T -2 Q4: A vertical magnet is dropped from position on the axis of a fixed metallic coil as shown in Figure, figure (i). In figure (ii) the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are ?? ?? and ?? ?? respectively then Page 3 JEE Solved Example on Electromagnetic Induction and Alternating Current JEE Mains Q1: A conducting loop of radius ?? is present in a uniform magnetic field ?? perpendicular to the plane of the ring. If radius ?? varies as a function of time't', as ?? = ?? ?? + ?? . The e.m.f. induced in the loop is (A) ?? ?? (?? ?? + ?? )?? clockwise (B) ?? (?? ?? + ?? )?? clockwise (C) ?? ?? (?? ?? + ?? )?? anticlockwise (D) zero Ans:(?? )?? = ?? ?? 2 = ?? (?? 0 + ?? ) 2 ???? ???? = 2?? (?? 0 + ?? ) ?? = -?????? ???? = -2???? (?? 0 + ?? ) ? 2?? (?? 0 + ?? )?? is induced anticlockwise. Note: To have clarity about clockwise or anticlockwise, remember as flux increases, it tries to reduce net magnetic field ?? . Hence voltage is induced. It leads to current in direction of voltage, which reduces magnetic field. Q2: A square wire loop of ???? .?? ???? side lies at right angle to a uniform magnetic field of ???? ?? . A 10V light bulb is in a series with the loop as shown in the Figure. The magnetic field is decreasing steadily to zero over a time interval ?? ?? . The bulb will shine full brightness if ?? ?? is equal to (A) 20 ms (B) 0.02 ms (C) 2 ms (D) 0.2 ms Ans:(?? )?? = ???? ??? 10 = 20× (0.1) 2 ??? ? ??? = 20 ms Q3: The dimensions of permeability of free space can be given by (A) [?????? -?? ?? -?? ] (B) [???? ?? -?? ] (C) [???? -?? ?? ?? ?? ?? ] (D) [???? ?? -?? ] Ans : (A) [MA -1 T -2 ] Now ?? = ?? 0 i 2?? (for circular wire) ? [?? 0 ] = [?? ][r] [i] = [MA -1 T -1 ][L] [A] = MLA -2 T -2 Q4: A vertical magnet is dropped from position on the axis of a fixed metallic coil as shown in Figure, figure (i). In figure (ii) the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are ?? ?? and ?? ?? respectively then (A) ?? ?? > ?? ,?? ?? > ?? (B) ?? ?? > ?? ,?? ?? < ?? (C) ?? ?? < ?? , ?? ?? < ?? (D) ?? ?? < ?? ,?? ?? > ?? Ans: (C) Induced emf tries to push the coil upward in case II and magnet in case-I, to present sudden change in net flux. ? a 1 ,a 2 < g Q5: A long metal bar of ???? ???? length is aligned along a north south line and moves eastward at a speed of 10 ???? -?? . A uniform magnetic field of ?? .?? ?? points vertically downwards. If the south end of the bar has a potential of ?? ?? , the induced potential at the end of the bar is (A) +???? ?? (B) -???? ?? (C) ?? ?? (D) Cannot be determined since there is not closed circuit Ans: (?? )?? = (?? ? × ?? ? )· l = [10??ˆ × (4?? ˆ )](0.3??ˆ)= 12 V Q6: A thin wire of length ?? ?? is perpendicular to the ???? plane. It is moved with velocity ??? ? = (?? ??ˆ + ?? ??ˆ + ?? ˆ )?? /?? through a region of magnetic induction ?? = (??ˆ + ?? ??ˆ) ???? /?? ?? . Then potential difference induced between the ends of the wire: (A) ?? ?? (B) ?? ?? (C) ?? ?? (D) none of these Page 4 JEE Solved Example on Electromagnetic Induction and Alternating Current JEE Mains Q1: A conducting loop of radius ?? is present in a uniform magnetic field ?? perpendicular to the plane of the ring. If radius ?? varies as a function of time't', as ?? = ?? ?? + ?? . The e.m.f. induced in the loop is (A) ?? ?? (?? ?? + ?? )?? clockwise (B) ?? (?? ?? + ?? )?? clockwise (C) ?? ?? (?? ?? + ?? )?? anticlockwise (D) zero Ans:(?? )?? = ?? ?? 2 = ?? (?? 0 + ?? ) 2 ???? ???? = 2?? (?? 0 + ?? ) ?? = -?????? ???? = -2???? (?? 0 + ?? ) ? 2?? (?? 0 + ?? )?? is induced anticlockwise. Note: To have clarity about clockwise or anticlockwise, remember as flux increases, it tries to reduce net magnetic field ?? . Hence voltage is induced. It leads to current in direction of voltage, which reduces magnetic field. Q2: A square wire loop of ???? .?? ???? side lies at right angle to a uniform magnetic field of ???? ?? . A 10V light bulb is in a series with the loop as shown in the Figure. The magnetic field is decreasing steadily to zero over a time interval ?? ?? . The bulb will shine full brightness if ?? ?? is equal to (A) 20 ms (B) 0.02 ms (C) 2 ms (D) 0.2 ms Ans:(?? )?? = ???? ??? 10 = 20× (0.1) 2 ??? ? ??? = 20 ms Q3: The dimensions of permeability of free space can be given by (A) [?????? -?? ?? -?? ] (B) [???? ?? -?? ] (C) [???? -?? ?? ?? ?? ?? ] (D) [???? ?? -?? ] Ans : (A) [MA -1 T -2 ] Now ?? = ?? 0 i 2?? (for circular wire) ? [?? 0 ] = [?? ][r] [i] = [MA -1 T -1 ][L] [A] = MLA -2 T -2 Q4: A vertical magnet is dropped from position on the axis of a fixed metallic coil as shown in Figure, figure (i). In figure (ii) the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are ?? ?? and ?? ?? respectively then (A) ?? ?? > ?? ,?? ?? > ?? (B) ?? ?? > ?? ,?? ?? < ?? (C) ?? ?? < ?? , ?? ?? < ?? (D) ?? ?? < ?? ,?? ?? > ?? Ans: (C) Induced emf tries to push the coil upward in case II and magnet in case-I, to present sudden change in net flux. ? a 1 ,a 2 < g Q5: A long metal bar of ???? ???? length is aligned along a north south line and moves eastward at a speed of 10 ???? -?? . A uniform magnetic field of ?? .?? ?? points vertically downwards. If the south end of the bar has a potential of ?? ?? , the induced potential at the end of the bar is (A) +???? ?? (B) -???? ?? (C) ?? ?? (D) Cannot be determined since there is not closed circuit Ans: (?? )?? = (?? ? × ?? ? )· l = [10??ˆ × (4?? ˆ )](0.3??ˆ)= 12 V Q6: A thin wire of length ?? ?? is perpendicular to the ???? plane. It is moved with velocity ??? ? = (?? ??ˆ + ?? ??ˆ + ?? ˆ )?? /?? through a region of magnetic induction ?? = (??ˆ + ?? ??ˆ) ???? /?? ?? . Then potential difference induced between the ends of the wire: (A) ?? ?? (B) ?? ?? (C) ?? ?? (D) none of these Ans:(?? )?? = (?? × ?? ? )· l = [(2??ˆ + 3??ˆ + ?? ˆ )× (??ˆ + 2??ˆ)](2?? ˆ )= [-2??ˆ + ??ˆ + ?? ˆ ][2?? ˆ ] ?? = 2?? Q7: The Figure shows an isosceles triangle wire frame with apex angle equal to ?? /?? . The frame starts entering into the uniform magnetic field ?? with Constant velocity ?? at ?? = ?? . The longest side of the frame is perpendicular to the direction of velocity. If ?? is the instantaneous current through the frame then choose the alternative showing the correct variation of ?? with time. Ans: (D) Let the triangle travel a distance ?? along ?? in time ?? . Area of triangle in magnetic field ?? = 1 2 ?? (2?? )= ?? 2 ?? = ?? 2 ?? 2 ?? = -?????? ???? Page 5 JEE Solved Example on Electromagnetic Induction and Alternating Current JEE Mains Q1: A conducting loop of radius ?? is present in a uniform magnetic field ?? perpendicular to the plane of the ring. If radius ?? varies as a function of time't', as ?? = ?? ?? + ?? . The e.m.f. induced in the loop is (A) ?? ?? (?? ?? + ?? )?? clockwise (B) ?? (?? ?? + ?? )?? clockwise (C) ?? ?? (?? ?? + ?? )?? anticlockwise (D) zero Ans:(?? )?? = ?? ?? 2 = ?? (?? 0 + ?? ) 2 ???? ???? = 2?? (?? 0 + ?? ) ?? = -?????? ???? = -2???? (?? 0 + ?? ) ? 2?? (?? 0 + ?? )?? is induced anticlockwise. Note: To have clarity about clockwise or anticlockwise, remember as flux increases, it tries to reduce net magnetic field ?? . Hence voltage is induced. It leads to current in direction of voltage, which reduces magnetic field. Q2: A square wire loop of ???? .?? ???? side lies at right angle to a uniform magnetic field of ???? ?? . A 10V light bulb is in a series with the loop as shown in the Figure. The magnetic field is decreasing steadily to zero over a time interval ?? ?? . The bulb will shine full brightness if ?? ?? is equal to (A) 20 ms (B) 0.02 ms (C) 2 ms (D) 0.2 ms Ans:(?? )?? = ???? ??? 10 = 20× (0.1) 2 ??? ? ??? = 20 ms Q3: The dimensions of permeability of free space can be given by (A) [?????? -?? ?? -?? ] (B) [???? ?? -?? ] (C) [???? -?? ?? ?? ?? ?? ] (D) [???? ?? -?? ] Ans : (A) [MA -1 T -2 ] Now ?? = ?? 0 i 2?? (for circular wire) ? [?? 0 ] = [?? ][r] [i] = [MA -1 T -1 ][L] [A] = MLA -2 T -2 Q4: A vertical magnet is dropped from position on the axis of a fixed metallic coil as shown in Figure, figure (i). In figure (ii) the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are ?? ?? and ?? ?? respectively then (A) ?? ?? > ?? ,?? ?? > ?? (B) ?? ?? > ?? ,?? ?? < ?? (C) ?? ?? < ?? , ?? ?? < ?? (D) ?? ?? < ?? ,?? ?? > ?? Ans: (C) Induced emf tries to push the coil upward in case II and magnet in case-I, to present sudden change in net flux. ? a 1 ,a 2 < g Q5: A long metal bar of ???? ???? length is aligned along a north south line and moves eastward at a speed of 10 ???? -?? . A uniform magnetic field of ?? .?? ?? points vertically downwards. If the south end of the bar has a potential of ?? ?? , the induced potential at the end of the bar is (A) +???? ?? (B) -???? ?? (C) ?? ?? (D) Cannot be determined since there is not closed circuit Ans: (?? )?? = (?? ? × ?? ? )· l = [10??ˆ × (4?? ˆ )](0.3??ˆ)= 12 V Q6: A thin wire of length ?? ?? is perpendicular to the ???? plane. It is moved with velocity ??? ? = (?? ??ˆ + ?? ??ˆ + ?? ˆ )?? /?? through a region of magnetic induction ?? = (??ˆ + ?? ??ˆ) ???? /?? ?? . Then potential difference induced between the ends of the wire: (A) ?? ?? (B) ?? ?? (C) ?? ?? (D) none of these Ans:(?? )?? = (?? × ?? ? )· l = [(2??ˆ + 3??ˆ + ?? ˆ )× (??ˆ + 2??ˆ)](2?? ˆ )= [-2??ˆ + ??ˆ + ?? ˆ ][2?? ˆ ] ?? = 2?? Q7: The Figure shows an isosceles triangle wire frame with apex angle equal to ?? /?? . The frame starts entering into the uniform magnetic field ?? with Constant velocity ?? at ?? = ?? . The longest side of the frame is perpendicular to the direction of velocity. If ?? is the instantaneous current through the frame then choose the alternative showing the correct variation of ?? with time. Ans: (D) Let the triangle travel a distance ?? along ?? in time ?? . Area of triangle in magnetic field ?? = 1 2 ?? (2?? )= ?? 2 ?? = ?? 2 ?? 2 ?? = -?????? ???? ???? = ?? ?? ???? (?? 2 ?? 2 ) ?? = 2?? ?? 2 ?? ?? ? ?? ? ?? Q7: Two identical coaxial circular loops carry a current I each circulating in the same direction. If the loops approach each other (A) The current in each will decrease (B) The current in each will increase (C) The current in each will remain the same (D) The current in one will increase and in other will decrease Ans : (A) For a circular loop B at center is greater than ?? at any point along the axis. When both the loops approach each other, magnetic field (B) starts increasing at center. To compensate it, Current decreasing. Q8: A copper rod ???? of length ?? , pivoted at one end A, rotates at constant angular velocity ?? , at right angle to a uniform magnetic field of induction B. The e.m.f. developed between the midpoint ?? to of the rod and end ?? is (A) ???? ?? ?? ?? (B) ???? ?? ?? ?? (C) ?? ???? | ?? ?? (D) ?? ???? ?? ?? ?? Ans: (D) d?? = ???? dl V = l?? ? d ?= B?? ldl E = B?? ? ldl = B?? l 2 2 | l 1 l 2 l 2 = L; l 1 = L 2 ? I ˆ = B?? 2 ( L 2 - ( L 2 ) 2 ) = 3 B?? l 2 8Read More
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