Skip to content

#vector

15 public questions tagged with this topic.

A magnetic dipole of moment \( 0.3 \, \text{A m}^2 \) is in a uniform field of \( 0.7 \, \text{T} \) at \( 30^\circ \).

**Axial versus equatorial** field comparison shows B_axial = 2 B_eq for same r. Using μ₀ = 4π×10⁻⁷ T·m/A, calculation involves r³ = (0.3)³ = 0.027 m³, so B = 10⁻⁷·m/r³ yields moment estimation. Torque is tau = m B sinθ . Given: m = 0.3 A m² , B = 0.7 T , θ = 30° , sin 30° = 0.5 . Substitute: tau = 0.3 × 0.7 × 0.5 = 0.105 N m . Substituting values gives 0.105 N m, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Magnetic Field Due to Bar Magnet - Axial and Equatorial

A 4kg particle moves with velocity v\=5j^m/s at r\=−3i^m. What is the magnitude of its angular momentum about the origin

L = r×p = |i^j^k^−300050| = k^((−3)×5−0×0) = −15k^kg m2/s. Magnitude = 15kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 15 kg m²/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

A particle starts from rest with a constant acceleration of (−2i^+5j^)m/s2. What is the magnitude of its velocity after

Velocity v=v0+at, with v0=0. As per NCERT Chapter 3, equations v=u+at, s=ut+½at², v²=u²+2as describe uniformly accelerated motion. Applying correct signs and units gives 16.16 m/s as the result, so option A is correct.

Ref: NCERT Class 11 Physics > Chapter 3: Motion in a Straight Line > Topic: Straight Line Motion - Mixed Concepts