A long solenoid of radius 4 cm has 1500 turns/m and carries a current of 3 A. A straight wire carrying 10 A is placed parallel to the axis of the solenoid at a distance of 8 cm from it.
(A) The magnitude of the magnetic field at the center of the solenoid is 4500 μT
(B) At the axis of the solenoid, the magnetic field due to straight wire is 25 μT
(C) The net magnetic field on the solenoid axis is the vector sum of the magnetic fields from the solenoid and the straight wire.
(D) Outside the solenoid, magnetic field due to the solenoid is approximately zero.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B), (C) and (D) only
Inside a long solenoid the field is uniform and along the axis, \( B = \mu_0 nI \), and outside it is nearly zero. A long straight wire produces circular field lines around itself, of magnitude \( \mu_0 I/2\pi d \). The solenoid does not screen the field of the wire.
(A) The magnitude of the magnetic field at the center of the solenoid is 4500 μT — Incorrect.
\( B = \mu_0 nI = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \times 1500\,\mathrm{m^{-1}} \times 3\,\mathrm{A} \)
\( B \approx 5.65\times10^{-3}\,\mathrm{T} \approx 5655\,\mu\mathrm{T} \)
(B) At the axis of the solenoid, the magnetic field due to straight wire is 25 μT — Correct. The axis is 8 cm from the wire.
\( \displaystyle B_w = \frac{\mu_0 I}{2\pi d} = \frac{2\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \times 10\,\mathrm{A}}{0.08\,\mathrm{m}} \)
\( B_w = 2.5\times10^{-5}\,\mathrm{T} = 25\,\mu\mathrm{T} \)
(C) The net magnetic field on the solenoid axis is the vector sum of the magnetic fields from the solenoid and the straight wire. — Correct. By the principle of superposition, magnetic fields add as vectors. Here the two fields are perpendicular: the solenoid’s field is along the axis, while the wire’s field circles the wire at right angles to it.
(D) Outside the solenoid, magnetic field due to the solenoid is approximately zero. — Correct. For a long solenoid the returning field lines spread over a very large region outside, so the field there is negligible.