11 a) A straight piece of conducting wire, 20 cm long, lies at 70°
a magnetic field of 1.8 × 10−5 T. A current, I, is allowed
to flow through it and it experiences a force of 0.01 N.
Calculate the value of I.
b) The wire in part (a) is bent into a rectangular shape so that
it has an area of 24 cm2
. Find the torque on the loop of wire
70° to the magnetic field of strength 1.8 × 10−5 T when the
same current as in part (a) flows through it.�
c) Find the magnetic dipole moment on a coil of wire with
1000 turns each of area 24 cm2
at 70° to a magnetic field
of strength 1.8 × 10−5 T with the same current as part (a)
flowing through the coil.�
a) The force on a current-carrying wire in a magnetic field is given by the equation F = BILsinθ, where B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field. We are given the values for L, θ, B, and F, and we need to solve for I.
F = BILsinθ
0.01 N = (1.8 × 10−5 T)(0.2 m)Isin70°
I = 0.01 N / [(1.8 × 10−5 T)(0.2 m)sin70°]
I ≈ 0.98 A
b) The torque on a current-carrying loop in a magnetic field is given by the equation τ = BIAN, where B is the magnetic field strength, I is the current, A is the area of the loop, N is the number of turns in the loop, and θ is the angle between the normal to the loop and the magnetic field. We are given the value for A, θ, B, and I, and we need to solve for τ.
τ = BIANsinθ
τ = (1.8 × 10−5 T)(0.24 m2)(1)(sin70°)(0.98 A)
τ ≈ 4.6 × 10−6 Nm
c) The magnetic dipole moment of a current-carrying loop is given by the equation μ = NIΑ, where N is the number of turns in the loop, I is the current, A is the area of the loop, and θ is the angle between the normal to the loop and the magnetic field. We are given the values for N, A, θ, B, and I, and we need to solve for μ.
μ = NIΑcosθ
μ = (1000)(0.24 m2)(0.98 A)cos70°
μ ≈ 7.3 × 10−2 Am2