A conducting rod of length 2√5 m and mass 4 kg rests on a horizontal plane. The friction coefficient is μ = 1/2. It carries current I = 2 A. Find the minimum magnetic-field magnitude (in T) required to start translation along the x-axis, g = 10 m s⁻². [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A conducting rod of length 2√5 m and mass 4 kg rests on a horizontal plane. The friction coefficient is μ = 1/2. It carries current I = 2 A. Find the minimum magnetic-field magnitude (in T) required to start translation along the x-axis, g = 10 m s⁻². [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The current-bearing rod experiences a magnetic force with magnitude F = IℓB; suitable magnetic-field direction can produce both horizontal driving force Fₓ and upward component Fᵧ, reducing the floor normal force. Step 2 — At limiting static friction, Fₓ = μ(mg−Fᵧ), so Fₓ + μFᵧ = μmg. Step 3 — For fixed vector force magnitude, the maximum possible Fₓ+μFᵧ is F√(1+μ²). Therefore minimum required F = μmg/√(1+μ²). Step 4 — With μ = 1/2, m = 4 kg, g = 10 m s⁻²: Fₘᵢₙ = (20)/√(5/4) = 40/√5 N.…