Physics · Textbook solutions

Magnetism

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 20 questions

12. Magnetism — worked examples

3 q

Solved Examples

Worked · 3
  1. Solved Ex.12.1
    A short magnetic dipole has magnetic moment 0.5 A m2^{2}. Calculate its magnetic field at a distance of 20 cm from the centre of magnetic dipole on (i) the axis (ii) the equatorial line (Given μ0=4π×10−7\mu_{0} = 4\pi \times 10^{-7} SI units)
  2. Solved Ex.12.2
    Earth's magnetic field at the equator is approximately 4×10−54 \times 10^{-5} T. Calculate Earth's dipole moment. (Radius of Earth =6.4×106= 6.4 \times 10^{6} m, μ0=4π×10−7\mu_{0} = 4\pi \times 10^{-7} SI units)
  3. Solved Ex.12.3
    At a given place on the Earth, a bar magnet of magnetic moment m⃗\vec{m} is kept horizontal in the East-West direction. P and Q are the two neutral points due to magnetic field of this magnet and B⃗H\vec{B}_{H} is the horizontal component of the Earth's magnetic field. (A) Calculate the angles between position vectors of P and Q with the direction of m⃗\vec{m}. (B) Points P and Q are 1 m from the centre of the bar magnet and BH=3.5×10−5 TB_{H} = 3.5 \times 10^{-5}\,\text{T}. Calculate the magnetic dipole moment of the bar magnet. Neutral point is that point where the resultant magnetic field is zero.

Exercises

17 q

Choose the correct option

Practice · 7
  1. Choose the correct option.
    Ex Q.1 (i)
    Let rr be the distance of a point on the axis of a bar magnet from its center. The magnetic field at rr is always proportional to
    1. A.
      1/r21/r^{2}
    2. B.
      1/r31/r^{3}
    3. C.
      1/r1/r
    4. D.
      not necessarily 1/r31/r^{3} at all points
  2. Ex Q.1 (ii)
    Magnetic meridian is the plane
    1. A.
      perpendicular to the magnetic axis of Earth
    2. B.
      perpendicular to geographic axis of Earth
    3. C.
      passing through the magnetic axis of Earth
    4. D.
      passing through the geographic axis Earth
  3. Ex Q.1 (iii)
    The horizontal and vertical component of magnetic field of Earth are same at some place on the surface of Earth. The magnetic dip angle at this place will be
    1. A.
      30∘30^{\circ}
    2. B.
      45∘45^{\circ}
    3. C.
      0∘0^{\circ}
    4. D.
      90∘90^{\circ}
  4. Ex Q.1 (iv)
    Inside a bar magnet, the magnetic field lines
    1. A.
      are not present
    2. B.
      are parallel to the cross sectional area of the magnet
    3. C.
      are in the direction from N pole to S pole
    4. D.
      are in the direction from S pole to N pole
  5. Ex Q.1 (v)
    A place where the vertical components of Earth's magnetic field is zero has the angle of dip equal to
    1. A.
      0∘0^{\circ}
    2. B.
      45∘45^{\circ}
    3. C.
      60∘60^{\circ}
    4. D.
      90∘90^{\circ}
  6. Ex Q.1 (vi)
    A place where the horizontal component of Earth's magnetic field is zero lies at
    1. A.
      geographic equator
    2. B.
      geomagnetic equator
    3. C.
      one of the geographic poles
    4. D.
      one of the geomagnetic poles
  7. Ex Q.1 (vii)
    A magnetic needle kept nonparallel to the magnetic field in a nonuniform magnetic field experiences
    1. A.
      a force but not a torque
    2. B.
      a torque but not a force
    3. C.
      both a force and a torque
    4. D.
      neither force nor a torque

Answer the following questions in brief

Practice · 2
  1. Answer the following questions in brief.
    Ex Q.2 (i)
    What happens if a bar magnet is cut into two pieces transverse to its length/ along its length?
  2. Ex Q.2 (ii)
    What could be the equation for Gauss' law of magnetism, if a monopole of pole strength p is enclosed by a surface?

Answer the following questions in detail

Practice · 3
  1. Answer the following questions in detail.
    Ex Q.3 (i)
    Explain the Gauss' law for magnetic fields.
  2. Ex Q.3 (ii)
    What is a geographic meridian. How does the declination vary with latitude? Where is it minimum?
  3. Ex Q.3 (iii)
    Define the Angle of Dip. What happens to angle of dip as we move towards magnetic pole from magnetic equator?

Solve the following problems

Practice · 5
  1. Solve the following Problems. [Take μ0=4π×10−7\mu_{0} = 4\pi \times 10^{-7} SI units, i.e. μ0/4π=10−7\mu_{0}/4\pi = 10^{-7} — the value stated by this chapter's own worked Examples 12.1 and 12.2. The exercise prints no constants line of its own.]
    Ex Q.4 (i)
    A magnetic pole of bar magnet with pole strength of 100 A m is 20 cm away from the centre of a bar magnet. Bar magnet has pole strength of 200 A m and has a length 5 cm. If the magnetic pole is on the axis of the bar magnet, find the force on the magnetic pole.
  2. Ex Q.4 (ii)
    A magnet makes an angle of 45∘45^{\circ} with the horizontal in a plane making an angle of 30∘30^{\circ} with the magnetic meridian. Find the true value of the dip angle at the place.
  3. Ex Q.4 (iii)
    Two small and similar bar magnets have magnetic dipole moment of 1.0 A m2^{2} each. They are kept in a plane in such a way that their axes are perpendicular to each other. A line drawn through the axis of one magnet passes through the center of other magnet. If the distance between their centers is 2 m, find the magnitude of magnetic field at the mid point of the line joining their centers.
  4. Ex Q.4 (iv)
    A circular magnet is made with its north pole at the centre, separated from the surrounding circular south pole by an air a gap. Draw the magnetic field lines in the gap. [The magnet is hypothetical magnet]. Draw a diagram to illustrate the magnetic lines of force between the south poles of two such magnets.
  5. Ex Q.4 (v)
    Two bar magnets are placed on a straight line with their north poles facing each other on a horizontal surface. Draw magnetic lines around them. Mark the position of any neutral points (points where there is no resultant magnetic field) on your diagram.