Tut Magnetic Fields

1

Tutorial Sheet : Magnetostatic Fields
Date of Upload : Oct 16, 2014
Learning Objectives:
1) Introduction with the magnetostatic fields.
2) Applications of Ampere’s circuit law and Biot-Savart’s law .
3) Solving boundary value problems for magnetic fields.
Attempt the following problems
1) Derive the expression of magnetic field intensity at a given point due to infinite sheet of current using Ampere’s circuit law.
−
→
−
→
→
2) Plane y=1 carries current K = 50− a z mA/m. Find H at (0, 0, 0) and (1, 5, −3).
−
→ −2ρ2 −
3) Given the magnetic vector potential A = 3 → a z Wb/m, calculate the total magnetic flux crossing the surface ϕ = π2 1 ≤ ρ ≤ 2 m, 0 ≤ z ≤ 5 m.
−
→
4) Calculate H at (3m, −6m, 2m) due to a current element of length 2 mm located at origin in free space that carries a current 16 mA in +y direction.
5) An infinitely long filamentary wire carries a current of 2 A in the +z direction. Calculate
−
→
• B at (−3, 4, 7).
◦
• The flux through the surface 2 ≤ ρ ≤ 6, ϕ = 90 0 ≤ z ≤ 4.
−
→
→
→
→
2 −
6) In a certain conducting region H = y z a x + 2(x + 1)yz − a y − (x + 1)z 2 − a z A/m, find
−
→
• J at (1, 4, 3).
• The current passing through y = 1, 0 ≤ x ≤ 1, 0 ≤ z ≤ 1.
→
−
→
−
→
7) For H = yz(x2 + y 2 )− a x − y 2 xz → a y + 4x2 y 2 − a z A/m, find
−
→
• J at (5, 2, −3).
• The current passing through x = −1, 0 ≤ y, z ≤ 2.
−
→
• Show that ∇ · B = 0.
8) Region 1, described by 3x + 4y ≥ 10, is free space, whereas region 2 described by 3x + 4y ≤ 10 is magnetic material with µ = 10µ0 . Assuming that boundary between material and free space is
−
→
−
→
→
→
→
current free, find B 2 if B 1 = 0.1− a x + 0.4− a y + 0.2− a z W b/m2 .
→
−
→
−
−
→
−
→
9) Given that H = 24 a x − 30 a y + 40 a z kA/m in region 1, z > 0 with µr = 50. If z = 0 separates
−
→
→
the region 1 and 2 and carries 6− a x kA/m, determine H in region 2, z < 0 with µr = 100.
10) State and prove Maxwell’s equations for static fields.
Note: Submit by : 28 Oct, 2014.