PYQ Vault

Physics · Textbook solutions

Moving Charges and Magnetism

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 26 questions

Worked Examples

12 q

Solved Examples

Worked · 12
  1. Eg 4.1
    A straight wire of mass 200 g200\,\text{g} and length 1.5 m1.5\,\text{m} carries a current of 2 A2\,\text{A}. It is suspended in mid-air by a uniform horizontal magnetic field B\mathbf{B} (Fig. 4.3). What is the magnitude of the magnetic field?
  2. Eg 4.2
    If the magnetic field is parallel to the positive yy-axis and the charged particle is moving along the positive xx-axis (Fig. 4.4), which way would the Lorentz force be for (a) an electron (negative charge), (b) a proton (positive charge).
  3. Eg 4.3
    What is the radius of the path of an electron (mass 9×10−31 kg9 \times 10^{-31}\,\text{kg} and charge 1.6×10−19 C1.6 \times 10^{-19}\,\text{C}) moving at a speed of 3×107 m/s3 \times 10^{7}\,\text{m/s} in a magnetic field of 6×10−4 T6 \times 10^{-4}\,\text{T} perpendicular to it? What is its frequency? Calculate its energy in keV. (1 eV=1.6×10−19 J1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}).
  4. Eg 4.4
    An element Δl=Δx i^\Delta \boldsymbol{l} = \Delta x\,\hat{\mathbf{i}} is placed at the origin and carries a large current I=10 AI = 10\,\text{A} (Fig. 4.8). What is the magnetic field on the yy-axis at a distance of 0.5 m0.5\,\text{m}. Δx=1 cm\Delta x = 1\,\text{cm}.
  5. Eg 4.5
    A straight wire carrying a current of 12 A12\,\text{A} is bent into a semi-circular arc of radius 2.0 cm2.0\,\text{cm} as shown in Fig. 4.11(a). Consider the magnetic field B\mathbf{B} at the centre of the arc. (a) What is the magnetic field due to the straight segments? (b) In what way the contribution to B\mathbf{B} from the semicircle differs from that of a circular loop and in what way does it resemble? (c) Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in Fig. 4.11(b)?
  6. Eg 4.6
    Consider a tightly wound 100100 turn coil of radius 10 cm10\,\text{cm}, carrying a current of 1 A1\,\text{A}. What is the magnitude of the magnetic field at the centre of the coil?
  7. Eg 4.7
    Figure 4.13 shows a long straight wire of a circular cross-section (radius aa) carrying steady current II. The current II is uniformly distributed across this cross-section. Calculate the magnetic field in the region r<ar < a and r>ar > a.
  8. Eg 4.8
    A solenoid of length 0.5 m0.5\,\text{m} has a radius of 1 cm1\,\text{cm} and is made up of 500500 turns. It carries a current of 5 A5\,\text{A}. What is the magnitude of the magnetic field inside the solenoid?
  9. Eg 4.9
    The horizontal component of the earth's magnetic field at a certain place is 3.0×10−5 T3.0 \times 10^{-5}\,\text{T} and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1 A1\,\text{A}. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is (a) east to west; (b) south to north?
  10. Eg 4.10
    A 100100 turn closely wound circular coil of radius 10 cm10\,\text{cm} carries a current of 3.2 A3.2\,\text{A}. (a) What is the field at the centre of the coil? (b) What is the magnetic moment of this coil? The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A uniform magnetic field of 2 T2\,\text{T} in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90∘90^{\circ} under the influence of the magnetic field. (c) What are the magnitudes of the torques on the coil in the initial and final position? (d) What is the angular speed acquired by the coil when it has rotated by 90∘90^{\circ}? The moment of inertia of the coil is 0.1 kg m20.1\,\text{kg m}^{2}.
  11. Eg 4.11
    (a) A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself (i.e., turns about the vertical axis). (b) A current-carrying circular loop is located in a uniform external magnetic field. If the loop is free to turn, what is its orientation of stable equilibrium? Show that in this orientation, the flux of the total field (external field + field produced by the loop) is maximum. (c) A loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible, why does it change to a circular shape?
  12. Eg 4.12
    In the circuit (Fig. 4.23) the current is to be measured. What is the value of the current if the ammeter shown (a) is a galvanometer with a resistance RG=60.00 ΩR_G = 60.00\,\Omega; (b) is a galvanometer described in (a) but converted to an ammeter by a shunt resistance rs=0.02 Ωr_s = 0.02\,\Omega; (c) is an ideal ammeter with zero resistance? The circuit is a 3.00 V3.00\,\text{V} source in series with a 3.00 Ω3.00\,\Omega resistor and the ammeter.

Exercises

14 q
  1. Ex 4.1
    A circular coil of wire consisting of 100100 turns, each of radius 8.0 cm8.0\,\text{cm} carries a current of 0.40 A0.40\,\text{A}. What is the magnitude of the magnetic field B\mathbf{B} at the centre of the coil?
  2. Ex 4.2
    A long straight wire carries a current of 35 A35\,\text{A}. What is the magnitude of the field B\mathbf{B} at a point 20 cm20\,\text{cm} from the wire?
  3. Ex 4.3
    A long straight wire in the horizontal plane carries a current of 50 A50\,\text{A} in north to south direction. Give the magnitude and direction of B\mathbf{B} at a point 2.5 m2.5\,\text{m} east of the wire.
  4. Ex 4.4
    A horizontal overhead power line carries a current of 90 A90\,\text{A} in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m1.5\,\text{m} below the line?
  5. Ex 4.5
    What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A8\,\text{A} and making an angle of 30∘30^{\circ} with the direction of a uniform magnetic field of 0.15 T0.15\,\text{T}?
  6. Ex 4.6
    A 3.0 cm3.0\,\text{cm} wire carrying a current of 10 A10\,\text{A} is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T0.27\,\text{T}. What is the magnetic force on the wire?
  7. Ex 4.7
    Two long and parallel straight wires A and B carrying currents of 8.0 A8.0\,\text{A} and 5.0 A5.0\,\text{A} in the same direction are separated by a distance of 4.0 cm4.0\,\text{cm}. Estimate the force on a 10 cm10\,\text{cm} section of wire A.
  8. Ex 4.8
    A closely wound solenoid 80 cm80\,\text{cm} long has 55 layers of windings of 400400 turns each. The diameter of the solenoid is 1.8 cm1.8\,\text{cm}. If the current carried is 8.0 A8.0\,\text{A}, estimate the magnitude of B\mathbf{B} inside the solenoid near its centre.
  9. Ex 4.9
    A square coil of side 10 cm10\,\text{cm} consists of 2020 turns and carries a current of 12 A12\,\text{A}. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30∘30^{\circ} with the direction of a uniform horizontal magnetic field of magnitude 0.80 T0.80\,\text{T}. What is the magnitude of torque experienced by the coil?
  10. Ex 4.10
    Two moving coil meters, M1M_1 and M2M_2 have the following particulars: R1=10 ΩR_1 = 10\,\Omega, N1=30N_1 = 30, A1=3.6×10−3 m2A_1 = 3.6 \times 10^{-3}\,\text{m}^{2}, B1=0.25 TB_1 = 0.25\,\text{T} R2=14 ΩR_2 = 14\,\Omega, N2=42N_2 = 42, A2=1.8×10−3 m2A_2 = 1.8 \times 10^{-3}\,\text{m}^{2}, B2=0.50 TB_2 = 0.50\,\text{T} (The spring constants are identical for the two meters). Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2M_2 and M1M_1.
  11. Ex 4.11
    In a chamber, a uniform magnetic field of 6.5 G6.5\,\text{G} (1 G=10−4 T1\,\text{G} = 10^{-4}\,\text{T}) is maintained. An electron is shot into the field with a speed of 4.8×106 m s−14.8 \times 10^{6}\,\text{m s}^{-1} normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e=1.5×10−19 Ce = 1.5 \times 10^{-19}\,\text{C}, me=9.1×10−31 kgm_e = 9.1 \times 10^{-31}\,\text{kg})
  12. Ex 4.12
    In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
  13. Ex 4.13(a)
    (a) A circular coil of 3030 turns and radius 8.0 cm8.0\,\text{cm} carrying a current of 6.0 A6.0\,\text{A} is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T1.0\,\text{T}. The field lines make an angle of 60∘60^{\circ} with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
  14. Ex 4.13(b)
    A circular coil of 3030 turns and radius 8.0 cm8.0\,\text{cm} carrying a current of 6.0 A6.0\,\text{A} is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T1.0\,\text{T}, the field lines making an angle of 60∘60^{\circ} with the normal of the coil, and a counter torque is applied to prevent the coil from turning. (b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)