Magnetic Field Due To Infinite Current Sheet MCQ Quiz - Objective Question with Answer for Magnetic Field Due To Infinite Current Sheet - Download Free PDF

Solution:

Magnetic field (B) generated by one sheet at the location of the second is given by:
B = (μ₀ K)/2 (direction parallel to the second sheet)

Force (F) acting on a sheet of width 'b' and length 'ℓ' is:
F = (b × K × ℓ) × (μ₀ K/2)

Force per unit area (P) is then:
P = F / (ℓ × b)
P = (μ₀ K²)/2

By substituting the given current per unit width (K = β / 2√π), we have:

P = (μ₀ / 2) × (β² / 4π)

⇒ P = (4π × 10⁻⁷) × (β² /8π) =2 × 10⁻⁷ N/m²

⇒ β = 2

Solution:

Magnetic field (B) generated by one sheet at the location of the second is given by:
B = (μ₀ K)/2 (direction parallel to the second sheet)

Force (F) acting on a sheet of width 'b' and length 'ℓ' is:
F = (b × K × ℓ) × (μ₀ K/2)

Force per unit area (P) is then:
P = F / (ℓ × b)
P = (μ₀ K²)/2

By substituting the given current per unit width (K = β / 2√π), we have:

P = (μ₀ / 2) × (β² / 4π)

⇒ P = (4π × 10⁻⁷) × (β² /8π) =2 × 10⁻⁷ N/m²

⇒ β = 2

Magnetic field

\(\rm \vec H = \frac{1}{2}\left( {\vec K \times {{\hat a}_n}} \right)\)

From the figure \(\rm \vec K = 4\ {A}/{m}\;{\hat a_x}\)

and \(\rm {\hat a_n} = - {\hat a_z}\)

Thus, \(\rm \vec H = \frac{1}{2}\left( {4{{\hat a}_x} \times \left( { - {{\hat a}_z}} \right)} \right)\)

\(\rm = \frac{1}{2} \times 4 \times {\hat a_y}\)

\(\rm \Rightarrow \vec H = 2{\hat a_y}\)