Physics · Textbook solutions

Magnetic Fields due to Electric Current

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 33 questions

10. Magnetic Fields due to Electric Current — worked examples

8 q

Solved Examples

Worked · 8
  1. Solved Ex.10.1
    A negatively charged particle travels with a velocity v⃗\vec{v} through a uniform magnetic field B⃗\vec{B} as shown in the following figure, in three different situations. What is the direction of the magnetic force F⃗m\vec{F}_m due to the magnetic field, on the particle?
  2. Solved Ex.10.2
    A particle of charge qq follows a trajectory as shown in the figure. Obtain the type of the charge (positive or negatively charged). Obtain the momentum pp of the particle in terms of B,L,s,qB, L, s, q, ss being the distance travelled by the particle. Particle trajectory: A uniform magnetic field B⃗\vec{B} is applied in the region pp', perpendicular to the plane of the paper, coming out of the plane of the paper.
  3. Solved Ex.10.3
    Consider a square loop of wire loaded with a glass bulb of mass mm hanging vertically, suspended in air with its one part in a uniform magnetic field B⃗\vec{B} with its direction coming out of the plane of the paper (⊙)(\odot). Due to the current II flowing through the loop, there is a magnetic force in upward direction. Calculate the current II in the loop for which the magnetic force would be exactly balanced by the force on mass mm due to gravity.
  4. Solved Ex.10.4
    A circular coil of conducting wire has 500 turns and an area 1.26×10−4 m21.26 \times 10^{-4}\ \mathrm{m}^2 is enclosed by the coil. A current 100 μA100\ \mu\mathrm{A} is passed through the coil. Calculate the magnetic moment of the coil.
  5. Solved Ex.10.5
    A wire has 2 straight sections and one arc as shown in the figure. Determine the direction and magnitude of the magnetic field produced at the centre O of the semicircle by the three sections individually and the total.
  6. Solved Ex.10.6
    Consider a closely wound 1000 turn coil, having radius of 1 m. If a current of 10 A passes through the coil, what will be the magnitude of the magnetic field at the centre?
  7. Solved Ex.10.7
    A coaxial cable consists of a central conducting core wire of radius aa and a coaxial cylindrical outer conductor of radius bb (see figure). The two conductors carry an equal current II in opposite directions in and out of the plane of the paper. What will be the magnitude of the magnetic field BB for (i) a<r<ba < r < b and (ii) b<rb < r? What will be its direction?
  8. Solved Ex.10.8
    A solenoid of length 25 cm has inner radius of 1 cm and is made up of 250 turns of copper wire. For a current of 3 A in it, what will be the magnitude of the magnetic field inside the solenoid?

Exercises

25 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (i)
    A conductor has 3 segments; two straight and of length LL each and a semicircular with radius RR. It carries a current II. What is the magnetic field BB at point P?
    1. A.
      μ04πIR\dfrac{\mu_0}{4\pi}\dfrac{I}{R}
    2. B.
      μ04πIR2\dfrac{\mu_0}{4\pi}\dfrac{I}{R^2}
    3. C.
      μ04IR\dfrac{\mu_0}{4}\dfrac{I}{R}
    4. D.
      μ0I4π\dfrac{\mu_0 I}{4\pi}
  2. Ex Q.1 (ii)
    Figure a, b show two Amperian loops associated with the conductors carrying current II in the sense shown. The ∮B⃗.dl⃗\displaystyle\oint \vec{B}.\mathrm{d}\vec{l} in the cases a and b will be, respectively,
    1. A.
      −μ0I-\mu_0 I, 0
    2. B.
      μ0I\mu_0 I, 0
    3. C.
      0, μ0I\mu_0 I
    4. D.
      0, −μ0I-\mu_0 I
  3. Ex Q.1 (iii)
    A proton enters a perpendicular uniform magnetic field BB at origin along the positive xx axis with a velocity v as shown in the figure. Then it will follow the following path. [The magnetic field is directed into the paper].
    1. A.
      It will continue to move along positive xx axis.
    2. B.
      It will move along a curved path, bending towards positive xx axis.
    3. C.
      It will move along a curved path, bending towards negative yy axis.
    4. D.
      It will move along a sinusoidal path along the positive xx axis.
  4. Ex Q.1 (iv)
    A conducting thick copper rod of length 1 m carries a current of 15 A and is located on the Earth's equator. There the magnetic flux lines of the Earth's magnetic field are horizontal, with the field of 1.3×10−41.3 \times 10^{-4} T, south to north. The magnitude and direction of the force on the rod, when it is oriented so that current flows from west to east, are
    1. A.
      14×10−414 \times 10^{-4} N, downward.
    2. B.
      20×10−420 \times 10^{-4} N, downward.
    3. C.
      14×10−414 \times 10^{-4} N, upward.
    4. D.
      20×10−420 \times 10^{-4} N, upward.
  5. Ex Q.1 (v)
    A charged particle is in motion having initial velocity v⃗\vec{v} when it enter into a region of uniform magnetic field perpendicular to v⃗\vec{v}. Because of the magnetic force the kinetic energy of the particle will
    1. A.
      remain uncharged.
    2. B.
      get reduced.
    3. C.
      increase.
    4. D.
      be reduced to zero.

Solve the following

Practice · 20
  1. Ex Q.2
    A piece of straight wire has mass 20 g and length 1 m. It is to be levitated using a current of 1 A flowing through it and a perpendicular magnetic field BB in a horizontal direction. What must be the magnetic of BB?
  2. Ex Q.3
    Calculate the value of magnetic field at a distance of 2 cm from a very long straight wire carrying a current of 5 A (Given: μ0=4π×10−7\mu_0 = 4\pi \times 10^{-7} Wb/Am).
  3. Ex Q.4
    An electron is moving with a speed of 3.2×1073.2 \times 10^{7} m/s in a magnetic field of 6.00×10−46.00 \times 10^{-4} T perpendicular to its path. What will be the radius of the path? What will be frequency and the kinetic energy in keV? [Given: mass of electron =9.1×10−31= 9.1 \times 10^{-31} kg, charge e=1.6×10−19e = 1.6 \times 10^{-19} C, 1 eV =1.6×10−19= 1.6 \times 10^{-19} J]
  4. Ex Q.5
    An alpha particle (the nucleus of helium atom) (with charge +2e+2e) is accelerated and moves in a vacuum tube with kinetic energy =10.00= 10.00 MeV. On applying a transverse a uniform magnetic field of 1.851 T, it follows a circular trajectory of radius 24.60 cm. Obtain the mass of the alpha particle. [charge of electron =1.62×10−19= 1.62 \times 10^{-19} C]
  5. Ex Q.6
    Two wires shown in the figure are connected in a series circuit and the same amount of current of 10 A passes through both, but in apposite directions. Separation between the two wires is 8 mm. The length AB is S=22S = 22 cm. Obtain the direction and magnitude of the magnetic field due to current in wire 2 on the section AB of wire 1. Also obtain the magnitude and direction of the force on wire 1. [μ0=4π×10−7\mu_0 = 4\pi \times 10^{-7} T.m/A]
  6. Ex Q.7
    A very long straight wire carries a current 5.2 A. What is the magnitude of the magnetic field at a distance 3.1 cm from the wire? [μ0=4π×10−7\mu_0 = 4\pi \times 10^{-7} T.m/A]
  7. Ex Q.8
    Current of equal magnitude flows through two long parallel wires having separation of 1.35 cm. If the force per unit length on each of the wires in 4.76×10−24.76 \times 10^{-2} N, what must be II?
  8. Ex Q.9
    Magnetic field at a distance 2.4 cm from a long straight wire is 16 μ\muT. What must be current through the wire?
  9. Ex Q.10
    The magnetic field at the centre of a circular current carrying loop of radius 12.3 cm is 6.4×10−66.4 \times 10^{-6} T. What will be the magnetic moment of the loop?
  10. Ex Q.11
    A circular loop of radius 9.7 cm carries a current 2.3 A. Obtain the magnitude of the magnetic field (a) at the centre of the loop and (b) at a distance of 9.7 cm from the centre of the loop but on the axis.
  11. Ex Q.12
    A circular coil of wire is made up of 100 turns, each of radius 8.0 cm. If a current of 0.40 A passes through it, what be the magnetic field at the centre of the coil?
  12. Ex Q.13
    For proton acceleration, a cyclotron is used in which a magnetic field of 1.4 Wb/m2^2 is applied. Find the time period for reversing the electric field between the two Ds.
  13. Ex Q.14
    A moving coil galvanometer has been fitted with a rectangular coil having 50 turns and dimensions 5 cm ×\times 3 cm. The radial magnetic field in which the coil is suspended is of 0.05 Wb/m2^2. The torsional constant of the spring is 1.5×10−91.5 \times 10^{-9} Nm/degree. Obtain the current required to be passed through the galvanometer so as to produce a deflection of 30∘30^\circ.
  14. Ex Q.15
    A solenoid of length π\pi m and 5 cm in diameter has winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at its centre along the axis.
  15. Ex Q.16
    A toroid of narrow radius of 10 cm has 1000 turns of wire. For a magnetic field of 5×10−25 \times 10^{-2} T along its axis, how much current is required to be passed through the wire?
  16. Ex Q.17
    In a cyclotron protons are to be accelerated. Radius of its D is 60 cm. and its oscillator frequency is 10 MHz. What will be the kinetic energy of the proton thus accelerated? (Proton mass =1.67×10−27= 1.67 \times 10^{-27} kg, e=1.6×10−19e = 1.6 \times 10^{-19} C, 1 eV =1.6×10−19= 1.6 \times 10^{-19} J)
  17. Ex Q.18
    A wire loop of the form shown in the figure carries a current II. Obtain the magnitude and direction of the magnetic field at P. (Given : B=μ0I4πR2B = \dfrac{\mu_0 I}{4\pi R}\sqrt{2} due to segment II)
  18. Ex Q.19
    Two long parallel wires going into the plane of the paper are separated by a distance RR, and carry a current II each in the same direction. Show that the magnitude of the magnetic field at a point P equidistant from the wires and subtending angle θ\theta from the plane containing the wires, is B=μ0πIRsin⁡2θB = \dfrac{\mu_0}{\pi}\dfrac{I}{R}\sin 2\theta. What is the direction of the magnetic field?
  19. Ex Q.20
    Figure shows a section of a very long cylindrical wire of diameter aa, carrying a current II. The current density which is in the direction of the central axis of the wire varies linearly with radial distance rr from the axis according to the relation J=J0 r/aJ = J_0\, r/a. Obtain the magnetic field BB inside the wire at a distance rr from its centre.
  20. Ex Q.21
    In the above problem, what will be the magnetic field BB inside the wire at a distance rr from its axis, if the current density JJ is uniform across the cross section of the wire?