Physics

When a charged particle moves perpendicular to a uniform magnetic field, it experiences a centripetal force equal to the magnetic Lorentz force qvB. Equating mv^2/R = qvB and solving for R gives R = mv/(qB).

A galvanometer is an instrument used to measure the current flowing through a circuit, not just detect its presence. It provides a quantitative measurement of current, typically small currents, by deflection of a needle.

Given vectors A = 3i + 2j - k and B = 3i - 2j + k, the dot product is calculated as (3)(3) + (2)(-2) + (-1)(1) = 9 - 4 - 1 = 4, which is not zero. Therefore, vectors A and B are not perpendicular, so option D is incorrect. B is not a negative vector of A (which would mean B = -A), so option B is incorrect. B does not have a negative magnitude since magnitude is always positive, so option C is incorrect. However, B is exactly the negative of A, i.e., B = -A, which means B is anti-parallel to A. Hence, option A is correct.

The self-inductance L of a coil is given by the formula L = emf / (rate of change of current). Given an induced emf of 2 V and a rate of change of current of 4 A/s, the self-inductance is L = 2 V / 4 A/s = 0.5 H. However, the options given include 0.5 mH (0.0005 H) and 0.5 H. The correct calculation yields 0.5 H, which corresponds to option B, not A. The original explanation had a mismatch between the calculation and the option letter. Therefore, the correct answer is B (0.5 H).

In a capacitive circuit, the current leads the voltage by 90 degrees (π/2 radians) because the capacitor causes the current to change before the voltage does. This is a fundamental property of capacitors in AC circuits.

In three-dimensional space, the direction of a vector is specified by two angles, often called direction cosines or angles with respect to coordinate axes. Three angles would be redundant, and one angle or no angle are insufficient to specify direction in space.

The greatest accuracy in measuring unknown resistance using a slide wire bridge is achieved when the balance point is near the middle of the wire. This ensures that the lengths on either side are nearly equal, minimizing errors due to wire non-uniformity and maximizing measurement precision.

Electromagnetic waves emitted from an antenna are transverse waves because their oscillations are perpendicular to the direction of wave propagation. They are not stationary or longitudinal waves.

When a current-carrying conductor is placed in a magnetic field parallel to it, the angle θ between the conductor and the magnetic field is 0°. The magnetic force is given by F = BIL sinθ. Since sin0° = 0, the force experienced by the conductor is zero.

A magnetic compass needle aligns with magnetic fields, which are produced by moving charges (currents). A charge at rest does not produce a magnetic field, so only a charge in motion can deflect the compass needle.

An inductor stores energy in its magnetic field created by the current flowing through its coils. It does not store energy in an electric field.

When a capacitor of capacitance C is charged by a constant current I, the voltage V across the capacitor increases linearly with time t according to the formula V = (I/C) * t. Rearranging for time, t = (C * V) / I. Substituting the given values: C = 30 µF = 30 × 10⁻⁶ F, V = 300 V, and I = 10 mA = 10 × 10⁻³ A, we get t = (30 × 10⁻⁶ F * 300 V) / (10 × 10⁻³ A) = 0.9 seconds. Therefore, the time taken for the potential difference to reach 300 V is 0.9 seconds, which corresponds to option A.

The question asks for the minimum current required to produce a 1 mm deflection at 1 meter distance, which corresponds to the current sensitivity of the galvanometer, typically expressed in milliamperes (mA). Among the options, '1 m A' (1 milliampere) is the correct numerical value representing this minimum current. Option C, 'current sensitivity,' is a concept, not a numerical value, so it cannot be the correct answer here.

The cross product of the unit vectors $\hat{i}$ and $\hat{j}$ is $\hat{k}$, following the right-hand rule in vector algebra.

In a radial magnetic field, the coil of a galvanometer is positioned so that the magnetic field lines are always radial to the coil's rotation axis. This arrangement ensures that the angle between the coil plane and the magnetic field is always 90°, making the deflecting torque proportional to BINA sinα, where α = 90°, so sinα = 1. Therefore, the torque is always BINA sin90° = BINA, meaning the torque depends on BINA sinα. Hence, the correct expression is BINA sinα.

The vectors $𝐢,𝐣,𝐤$ are unit vectors along the x, y, and z axes respectively. The cross product $𝐣\times 𝐤=𝐢$, which is a unit vector. The dot product $𝐢\cdot 𝐢=1$, so the magnitude is 1.

The magnetic force on a current-carrying wire is given by F = BIL sinθ. Here, θ = 90°, so sinθ = 1. Rearranging, I = F / (B * L) = 5 N / (0.5 T * 0.1 m) = 100 A.

Two parallel wires carrying currents in opposite directions produce magnetic fields that cause the wires to repel each other due to the Lorentz force between the currents.

When a charged particle enters a uniform magnetic field with a velocity component both perpendicular and parallel to the field, it undergoes circular motion perpendicular to the field and uniform motion parallel to the field, resulting in a helical (spiral) trajectory.

In a parallel circuit, all components share the same two nodes, so the potential difference (voltage) across each component is the same regardless of their individual impedances. Therefore, the voltage across the inductor and capacitor connected in parallel is the same as the applied sinusoidal voltage.

The magnitude of vector A = 2i - 2j + k is calculated as √(2² + (-2)² + 1²) = √(4 + 4 + 1) = √9 = 3. The unit vector in the direction of A is the vector divided by its magnitude, which is (2i - 2j + k)/3. Therefore, the correct option is C.

Electromechanical instruments are devices that combine electrical and mechanical components to measure or indicate electrical quantities. A galvanometer is an electromechanical instrument that measures small electric currents by deflecting a pointer. Voltmeters and ammeters are also electromechanical instruments, often using galvanometer mechanisms with additional components to measure voltage and current respectively. However, an AC transformer and a DC generator are electrical machines used to convert electrical energy or generate electricity, not instruments used for measurement. Therefore, the correct answer is D, as it is not an electromechanical instrument in the context of measurement devices.

When an electron moves perpendicular to a uniform magnetic field, the magnetic force acts as a centripetal force, causing the electron to move in a circular path in the plane perpendicular to the field.

If A = B, then their dot products with their unit vectors should be equal, but A.B = A^ B^ is not a valid equality since A^ and B^ are unit vectors and the dot product of A and B is not equal to the product of their unit vectors. The other options correctly state properties that hold when A = B.

The radius r of the circular path of a charged particle moving perpendicular to a uniform magnetic field is given by r = mv/(qB). This shows that r is directly proportional to the mass m, and inversely proportional to the charge q and magnetic field B. Therefore, the radius increases with increasing mass.