Page 1 Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 Ë† E E k ?? ? and magnetic field 0 Ë† B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 Ë†Ë† v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis. At time t = 0, it is given a velocity v 0 at an angle ? with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the x-axis. A magnetic field 0 Ë†Ë† B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 Ë† Ë† Ë† B B (i j k) ? ? ? ? Solutions 1. (along negative z-direction) Electric field will make z-component of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm. Page 2 Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 Ë† E E k ?? ? and magnetic field 0 Ë† B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 Ë†Ë† v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis. At time t = 0, it is given a velocity v 0 at an angle ? with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the x-axis. A magnetic field 0 Ë†Ë† B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 Ë† Ë† Ë† B B (i j k) ? ? ? ? Solutions 1. (along negative z-direction) Electric field will make z-component of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm. Solutions 1. 2. Introductory Exercise 23.5 Q 1. (a) A conductor in the shape of a square of edge length l = 0.4 m carries a current i = 10.0 A. Calculate the magnitude and direction of magnetic field at the centre of the square. (b) If this conductor is formed into a single circular turn and carries the same current, what is the value of the magnetic field at the centre. Q 2. Determine the magnetic field at point P located a distance x from the corner of an infinitely long wire bent at right angle as shown in figure. The wire carries a steady current i. Q 3. A conductor consists of a circular loop of radius R = 10 cm and two straight, long sections as shown in figure. The wire lies in the plane of the paper and carries a current of i = 7.00 A. Determine the magnitude and direction of the magnetic field at the centre of the loop. Q 4. The segment of wire shown in figure carries a current of i = 5.0 A, where the radius of the circular arc is R = 3.0 cm. Determine the magnitude and direction of the magnetic field at the origin. (Fig.) Page 3 Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 Ë† E E k ?? ? and magnetic field 0 Ë† B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 Ë†Ë† v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis. At time t = 0, it is given a velocity v 0 at an angle ? with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the x-axis. A magnetic field 0 Ë†Ë† B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 Ë† Ë† Ë† B B (i j k) ? ? ? ? Solutions 1. (along negative z-direction) Electric field will make z-component of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm. Solutions 1. 2. Introductory Exercise 23.5 Q 1. (a) A conductor in the shape of a square of edge length l = 0.4 m carries a current i = 10.0 A. Calculate the magnitude and direction of magnetic field at the centre of the square. (b) If this conductor is formed into a single circular turn and carries the same current, what is the value of the magnetic field at the centre. Q 2. Determine the magnetic field at point P located a distance x from the corner of an infinitely long wire bent at right angle as shown in figure. The wire carries a steady current i. Q 3. A conductor consists of a circular loop of radius R = 10 cm and two straight, long sections as shown in figure. The wire lies in the plane of the paper and carries a current of i = 7.00 A. Determine the magnitude and direction of the magnetic field at the centre of the loop. Q 4. The segment of wire shown in figure carries a current of i = 5.0 A, where the radius of the circular arc is R = 3.0 cm. Determine the magnitude and direction of the magnetic field at the origin. (Fig.) Q 5. Consider the current carrying loop shown in figure formed of radial lines and segments of circles whose centres are at point P. Find the magnitude and direction of B ? at point P. (Fig.) Q 6. Two long, parallel conductors carry currents i 1 = 3.0 A and i 2 = 3.0 A, both directed into the page. Determine the magnitude of the resultant magnetic field at point P. Q 7. A rectangular loop consists of N = 100 closed wrapped turns and has dimensions (0.4 m × 0.3 m). The loop is hinged along the y-axis and its plane makes an angle ? = 30? with the x-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field B = 0.8 T directed along the x-axis when current is i =1.2 A in the direction shown. What is the expected direction of rotation of the loop? Solutions 1. (a) From screw law, we can see that direction of magnetic field at centre of the square is inwards as the current is clockwise. Page 4 Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 Ë† E E k ?? ? and magnetic field 0 Ë† B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 Ë†Ë† v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis. At time t = 0, it is given a velocity v 0 at an angle ? with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the x-axis. A magnetic field 0 Ë†Ë† B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 Ë† Ë† Ë† B B (i j k) ? ? ? ? Solutions 1. (along negative z-direction) Electric field will make z-component of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm. Solutions 1. 2. Introductory Exercise 23.5 Q 1. (a) A conductor in the shape of a square of edge length l = 0.4 m carries a current i = 10.0 A. Calculate the magnitude and direction of magnetic field at the centre of the square. (b) If this conductor is formed into a single circular turn and carries the same current, what is the value of the magnetic field at the centre. Q 2. Determine the magnetic field at point P located a distance x from the corner of an infinitely long wire bent at right angle as shown in figure. The wire carries a steady current i. Q 3. A conductor consists of a circular loop of radius R = 10 cm and two straight, long sections as shown in figure. The wire lies in the plane of the paper and carries a current of i = 7.00 A. Determine the magnitude and direction of the magnetic field at the centre of the loop. Q 4. The segment of wire shown in figure carries a current of i = 5.0 A, where the radius of the circular arc is R = 3.0 cm. Determine the magnitude and direction of the magnetic field at the origin. (Fig.) Q 5. Consider the current carrying loop shown in figure formed of radial lines and segments of circles whose centres are at point P. Find the magnitude and direction of B ? at point P. (Fig.) Q 6. Two long, parallel conductors carry currents i 1 = 3.0 A and i 2 = 3.0 A, both directed into the page. Determine the magnitude of the resultant magnetic field at point P. Q 7. A rectangular loop consists of N = 100 closed wrapped turns and has dimensions (0.4 m × 0.3 m). The loop is hinged along the y-axis and its plane makes an angle ? = 30? with the x-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field B = 0.8 T directed along the x-axis when current is i =1.2 A in the direction shown. What is the expected direction of rotation of the loop? Solutions 1. (a) From screw law, we can see that direction of magnetic field at centre of the square is inwards as the current is clockwise. = 2.83 × 10 -5 T (b) 2 ?R = 4 (0.4) = 24.7 × 10 -6 T 2. Magnetic field due to horizontal wire is zero. Magnetic field due to vertical is 3. Both straight and circular wires will produce magnetic fields inwards. = 5.8 × 10 -5 T 4. Magnetic field at O due to two straight wires = 0 Magnetic field due to circular wire (due to whole circle) = 2.62 × 10 -5 T 5. Magnetic field at P due to straight wires = 0 Due to circular wires one is outwards (of radius a) and other is inwards. 60° means 1 th 6 of whole circle. (outwards) 6. Page 5 Introductory Exercise 23.3 Q 1. In a certain region uniform electric field 0 Ë† E E k ?? ? and magnetic field 0 Ë† B B k ?? ? are present. At time t = 0 a particle of mass m and charge q is given a velocity 00 Ë†Ë† v v j v k ?? ? . Find the minimum speed of the particle and the time when it happens so. Q 2. A particle of mass m and charge q is lying at the origin in a uniform magnetic field B directed along x-axis. At time t = 0, it is given a velocity v 0 at an angle ? with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution. Q 3. A wire of length l carries a current i along the x-axis. A magnetic field 0 Ë†Ë† B B (j k) ?? ? exists in the space. Find the magnitude of the magnetic force acting on the wire. Q 4. In the above problem will the answer change if magnetic field becomes 0 Ë† Ë† Ë† B B (i j k) ? ? ? ? Solutions 1. (along negative z-direction) Electric field will make z-component of velocity zero. At that time speed of the particle will be minimum and that minimum speed is the other component i. e., v 0 . This is minimum when, 2. Path is helix and after one rotation only x-coordinate will change by a distance equal to pitch. 3. 4. No it will not change, as the new component of is in the direction of Introductory Exercise 23.4 Q 1. A charge q is uniformly distributed on a nonconducting disc of radius Ft. It is rotated with an angular speed a about an axis passing through the centre of mass of the disc and perpendicular to its plane. Find the magnetic moment of the disc. [Hint: Magnetic moment = q 2m ?? ?? ?? (angular momentum)] Q 2. Find the magnetic moment of the current carrying loop OABCO shown in figure. Given that, i = 4.0 A, OA = 20 cm and AB =10 cm. Solutions 1. 2. Introductory Exercise 23.5 Q 1. (a) A conductor in the shape of a square of edge length l = 0.4 m carries a current i = 10.0 A. Calculate the magnitude and direction of magnetic field at the centre of the square. (b) If this conductor is formed into a single circular turn and carries the same current, what is the value of the magnetic field at the centre. Q 2. Determine the magnetic field at point P located a distance x from the corner of an infinitely long wire bent at right angle as shown in figure. The wire carries a steady current i. Q 3. A conductor consists of a circular loop of radius R = 10 cm and two straight, long sections as shown in figure. The wire lies in the plane of the paper and carries a current of i = 7.00 A. Determine the magnitude and direction of the magnetic field at the centre of the loop. Q 4. The segment of wire shown in figure carries a current of i = 5.0 A, where the radius of the circular arc is R = 3.0 cm. Determine the magnitude and direction of the magnetic field at the origin. (Fig.) Q 5. Consider the current carrying loop shown in figure formed of radial lines and segments of circles whose centres are at point P. Find the magnitude and direction of B ? at point P. (Fig.) Q 6. Two long, parallel conductors carry currents i 1 = 3.0 A and i 2 = 3.0 A, both directed into the page. Determine the magnitude of the resultant magnetic field at point P. Q 7. A rectangular loop consists of N = 100 closed wrapped turns and has dimensions (0.4 m × 0.3 m). The loop is hinged along the y-axis and its plane makes an angle ? = 30? with the x-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field B = 0.8 T directed along the x-axis when current is i =1.2 A in the direction shown. What is the expected direction of rotation of the loop? Solutions 1. (a) From screw law, we can see that direction of magnetic field at centre of the square is inwards as the current is clockwise. = 2.83 × 10 -5 T (b) 2 ?R = 4 (0.4) = 24.7 × 10 -6 T 2. Magnetic field due to horizontal wire is zero. Magnetic field due to vertical is 3. Both straight and circular wires will produce magnetic fields inwards. = 5.8 × 10 -5 T 4. Magnetic field at O due to two straight wires = 0 Magnetic field due to circular wire (due to whole circle) = 2.62 × 10 -5 T 5. Magnetic field at P due to straight wires = 0 Due to circular wires one is outwards (of radius a) and other is inwards. 60° means 1 th 6 of whole circle. (outwards) 6. B 1 and B 2 are mutually perpendicular at P = 1.3 × 10 -5 T 7. Torque vector and expected direction of rotation is shown in figure. Introductory Exercise 23.6 Q 1. Four long, parallel conductors carry equal currents of 5.0 A. The direction of the currents is into the page at points A and B and out of the page at C and D. Calculate the magnitude and direction of the magnetic field at point P, located at the centre of the square. Q 2. Figure given in the question is a cross-sectional view of a coaxial cable. The centre conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is surrounded by another rubber layer. The current in the inner conductor is 1.0 A out of the page, and the current in the outer conductor is 3.0 A into the page. Determine the magnitude and direction of the magnetic field at points a and b.Read More

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