13.2 Problems
591
13.40 Use Ampere’s law to calculate the magnetic field for a long cylindrical conductor of radius R and a current I flowing through it at a distance r from the
central axis of the conductor when (a) r > R and (b) r < R
13.41 Current I flows in two concentric circular arcs of radii r and 2r , Fig. 13.12.
Both arcs are quarter of a circle with P as the centre. Determine B at P.
[University of Durham]
Fig. 13.12
13.42 (a) A current I flows in a straight wire of length L. Show that the magnitude
of the magnetic field at a perpendicular distance x from the midpoint of
the wire is given by
|B| =
μ 0 I
4π
L
x
(L/2) 2 + x 2
where μ 0 is the permeability of free space. What is the direction of the
B field?
(b) A loop of wire of length l carries a current I . Compare the magnetic
fields at the centre of the loop when it is bent into (a) a square and (b) an
equilateral triangle.
[University of Durham 2000]
13.43 Two identical, parallel co-axial coils of radius r , and having N turns, are
separated by a distance r along their common axis. They both carry a current
I in the same direction. Derive an expression for the magnetic field on the
axis at the mid-point in between the coils. Evaluate the field when N = 100,
r = 20 cm and I = 2 A.
13.44 State the relationship between the tangential component of the magnetic field
B summed around a closed curve C and the current I c passing through the
area enclosed by the curve.
591
13.40 Use Ampere’s law to calculate the magnetic field for a long cylindrical conductor of radius R and a current I flowing through it at a distance r from the
central axis of the conductor when (a) r > R and (b) r < R
13.41 Current I flows in two concentric circular arcs of radii r and 2r , Fig. 13.12.
Both arcs are quarter of a circle with P as the centre. Determine B at P.
[University of Durham]
Fig. 13.12
13.42 (a) A current I flows in a straight wire of length L. Show that the magnitude
of the magnetic field at a perpendicular distance x from the midpoint of
the wire is given by
|B| =
μ 0 I
4π
L
x
(L/2) 2 + x 2
where μ 0 is the permeability of free space. What is the direction of the
B field?
(b) A loop of wire of length l carries a current I . Compare the magnetic
fields at the centre of the loop when it is bent into (a) a square and (b) an
equilateral triangle.
[University of Durham 2000]
13.43 Two identical, parallel co-axial coils of radius r , and having N turns, are
separated by a distance r along their common axis. They both carry a current
I in the same direction. Derive an expression for the magnetic field on the
axis at the mid-point in between the coils. Evaluate the field when N = 100,
r = 20 cm and I = 2 A.
13.44 State the relationship between the tangential component of the magnetic field
B summed around a closed curve C and the current I c passing through the
area enclosed by the curve.