Advertisements
Advertisements
Question
A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is ______.
Options
4 : 1
1 : 1
4 : 3
3 : 4
Advertisements
Solution
A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is 4 : 3.
Explanation:
At P2, B2 = `(mu_0I)/(2pi((3a)/2)) = (mu_0I)/(3pia)`
At P1, B1 = `(mu_0(I//4))/(2pi(a//2)) = (mu_0I)/(4pia)`
`therefore B_2/B_1 = (((mu_0I)/(3pia)))/(((mu_0I)/(4pia))) => B_2/B_1 = 4/3`
RELATED QUESTIONS
How are the magnetic field lines different from the electrostatic field lines?
A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10–2 J. What is the magnitude of magnetic moment of the magnet?
When iron filings are sprinkled on a sheet of glass placed over a short bar magnet then, the iron filings form a pattern suggesting that the magnet has ______.
Four point masses, each of value m, are placed at the comers of a square ABCD of side L, the moment of inertia of this system about an axis through A and parallel to BD is ______.
Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole p in an electrostatic field E and (ii) magnetic dipole m in a magnetic field B. Write down a set of conditions on E, B, p, m so that the two motions are verified to be identical. (Assume identical initial conditions.)
A bar magnet of magnetic moment m and moment of inertia I (about centre, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the midpoint, perpendicular to length, in a magnetic field B. What would be the similar period T′ for each piece?
Use (i) the Ampere’s law for H and (ii) continuity of lines of B, to conclude that inside a bar magnet, (a) lines of H run from the N pole to S pole, while (b) lines of B must run from the S pole to N pole.
