JEE Main Physics: Magnetic field along axis of circular coil Practice Questions

Correct answer: A — The direction of the magnetic field environment

The direction of the magnetic field along the axis of the coil is determined by applying the Right-Hand Rule, which explicitly relates the direction of the current flow to the orientation of the loop to find the direction of the resulting magnetic field.

Correct answer: B — Current flowing through the coil

The magnetic field along the axis of a circular coil is directly proportional to the current (I) flowing through the coil and inversely proportional to the radius (R) of the coil. However, among the choices given, the most direct proportionality is with the current.

Correct answer: A — 27

Since B ∝ R², if the radius R is tripled (3R), the magnetic field will increase by a factor of (3)² = 9.

Correct answer: D — 1/R

The magnetic field along the axis of a circular coil is inversely proportional to the radius of the coil (B ∝ 1/R).

Correct answer: A — It will be doubled

Since the magnetic field along the axis is directly proportional to the current (B ∝ I), if the current is doubled, the magnetic field along the axis will also be doubled.

Correct answer: A — B = μ₀ I

For a circular loop (coil) of radius R carrying current I, the magnetic field along its axis is given by B = (μ₀ I)/2R. (Note: Since the instruction asks for conceptual recall, this tests the primary relationship for a single loop axis).

Correct answer: D — √3:1

The magnetic field along the axis of a single coil in a uniform field B is Bₐₓᵢₛ = (2μ₀ I)/R cos θ. For the first coil, B₁ = (2μ₀ I)/R cos(30°). For the second coil, B₂ = (2μ₀ I)/R cos(60°). The ratio B₁/B₂ = (cos(30°))/(cos(60°)) = (√3/2)/(1/2) = √3.

Correct answer: D — (I₁ R₁²)/(R₁² + d²) - (I₂ R₂²)/(R₂² + d²)

The magnetic field along the axis of a single coil of radius R carrying current I at distance d is B = (μ₀ I R²)/(2(R² + d²)⁽3/2)). The difference between the fields of two coaxial coils (assuming the separation d is small compared to R₁, R₂) is calculated by subtracting their individual field expressions, which involves the ratio of R² over the distance term.

Correct answer: B — B = (μ₀ I)/2r (where I is the current in the loop)

When a circular loop (carrying current I) is placed perpendicular to the axis of a uniform magnetic field B, the field along the loop's axis is given by Bₐₓᵢₛ = (μ₀ I)/2r. This is the standard result for the field measured along the axis perpendicular to the loop.

Correct answer: D — (μ₀ I)/2R cos(60°)

The magnetic field along the axis of a coil is Bₐₓᵢₛ = (μ₀ I)/2R (cos θ₁ + cos θ₂). Since the field is zero at the center (implying the current distribution is symmetric), the field component along the axis depends solely on the angle θ between the coil plane and the field B⃗. When the axis is aligned with B⃗ (which is not the case here), the field is maximal. For a coil with zero field at the center, the field along the axis is Bₐₓᵢₛ = (μ₀ I)/2R cos θ, where θ is the angle between the plane of the coil and B⃗. Here, θ= 60°.

Correct answer: A — AB_(net) = (μ₀ I A)/2R + 0

For a single loop whose axis is parallel to B⃗, Bₐₓᵢₛ = 0. For a loop whose axis is perpendicular to B⃗, Bₐₓᵢₛ = (μ₀ I A)/2R. Since the field contributions along the common axis are calculated based on the components perpendicular to the axis, and the fields are oriented oppositely relative to the axis projection, the net field along the axis connecting the centers is zero.