Physics

The magnetic field strength inside a solenoid is given by B = μnI, where μ is the permeability, n is the number of turns per unit length, and I is the current. Option A is incorrect because it uses total turns N instead of turns per unit length n, and option B is incorrect due to incorrect formula structure. Therefore, option C is correct.

The dot product of two vectors A and B is calculated as the sum of the products of their corresponding components: AxBx + AyBy + AzBz. Option A correctly represents this formula.

When a shunt resistance is connected across a galvanometer and the deflection is reduced to half (from 50 divisions to 25 divisions), the galvanometer resistance (Rg) can be calculated using the formula: Rg = (n / (N - n)) * Rs, where N is the original deflection, n is the new deflection, and Rs is the shunt resistance. Here, N = 50, n = 25, and Rs = 12Ω. Substituting these values gives Rg = (25 / (50 - 25)) * 12Ω = (25 / 25) * 12Ω = 12Ω. Therefore, the galvanometer resistance is 12Ω, which corresponds to option D.

A current-carrying solenoid behaves like a bar magnet with a magnetic field along its axis. When suspended freely, it aligns itself along the Earth's magnetic field, coming to rest in the North-South direction due to magnetic torque.

For three coplanar forces to keep a body in equilibrium, they must be concurrent, meaning their lines of action intersect at a single point. This ensures both the net force and net moment about that point are zero, satisfying equilibrium conditions.

A null vector is defined as a vector with zero magnitude and no specific direction. Since both zero magnitude and no specified direction are true characteristics, option C is correct.

An electron moving through perpendicular electric and magnetic fields experiences forces from both fields. It will suffer no deflection if the electric force equals the magnetic force in magnitude but opposite in direction, which gives E = Bv (where v is the electron's velocity).

An electromagnetic wave consists of electric and magnetic fields oscillating perpendicular to each other and to the direction of wave propagation. This perpendicular arrangement is fundamental to the nature of electromagnetic waves.

For a sinusoidal alternating current, the peak current (I_peak) is related to the RMS current (I_rms) by the formula I_peak = I_rms × √2. Given I_rms = 4.0 A, the peak current is I_peak = 4.0 × 1.414 = 5.66 A approximately. The resistor value and frequency do not affect this calculation. Therefore, the correct answer is D (5.66 A).

For two equal forces F acting at an angle θ, the resultant is R = √(F² + F² + 2F²cosθ) = F√(2 + 2cosθ). Given R = F, so √(2 + 2cosθ) = 1. Squaring gives 2 + 2cosθ = 1, hence cosθ = -1/2. Therefore, θ = 120°.