The magnetic dipole moment (μ) is defined as the product of the current (I) flowing through a loop and the area (A) of the loop, μ = I × A.

Using the right-hand rule, if the magnetic field is into the paper and the charge moves to the right, the force will be upwards.

A magnetic field is produced by moving electric charges, such as those in a current-carrying wire.

Period (T) = 1 / frequency (f) = 1 / 1 Hz = 1 s.

The period T is the reciprocal of frequency f. Thus, T = 1/f = 1/2 = 0.5 s.

Period (T) = 1 / Frequency (f) = 1 / 2 Hz = 0.5 s.

Frequency (f) = (1/2π)√(k/m) => k = (2πf)² * m = (2π*3)² * 2 ≈ 18 N/m.

Frequency (f) = 1/(2π)√(k/m) => k = (2πf)²m = (2π × 3)² × 0.5 ≈ 18 N/m.

Frequency f = 1/T = 1/2 s = 0.5 Hz.

At the top, T + mg = mv²/L. T = mv²/L - mg.

The frequency f of a mass-spring system is given by f = (1/2π)√(k/m). Here, f = (1/2π)√(200/0.5) ≈ 2 Hz.

Angular frequency ω is related to frequency f by ω = 2πf. Therefore, for f = 1 Hz, ω = 2π(1) = 2π rad/s.

Period (T) = 1 / frequency = 1 / 2 Hz = 0.5 s.

Angular frequency ω = 2πf = 2π × 5 Hz = 10π rad/s.

The maximum speed v_max is given by v_max = Aω, where A is the amplitude and ω is the angular frequency. Thus, v_max = 0.1 * 20 = 2 m/s.

Poisson's ratio (ν) = - (lateral strain) / (longitudinal strain), thus the lateral contraction ratio is 0.3.

Temperature gradient = (T_hot - T_cold) / Length. Assuming length is 8 m, gradient = (100°C - 20°C) / 8 m = 10°C/m.

Using Fourier's law: Q/t = kA(ΔT/L) = 200 W/m°C * 0.0001 m² * (100°C/1 m) = 200 W.

Energy U = 1/2 C V^2. Initial U = 1/2 * 5 × 10^-6 * 10^2 = 0.025 J; Final U = 1/2 * 5 × 10^-6 * 20^2 = 0.1 J. Change = 0.1 - 0.025 = 0.075 J = 75 µJ.

Capacitance C is inversely proportional to the distance d between the plates. If d is halved, C doubles, so the new capacitance is 10μF.

Angular velocity ω = v/r.

Centripetal acceleration a_c = v²/r.

Frequency f = number of oscillations / time = 20 / 40 s = 0.5 Hz.

Time period (T) = 2π√(L/g) = 2π√(1/9.8) ≈ 2 s

Time period (T) = 2π√(L/g) ≈ 2π√(1/9.8) ≈ 2 s.

The potential energy of a pendulum is maximum at the highest point of its swing, where its kinetic energy is minimum.

Frequency (f) = 1 / (2π√(L/g)) = 1 / (2π√(1/9.8)) ≈ 1 Hz.

For small angles, T ≈ 2π√(L/g). Assuming L = 1 m, T ≈ 2π√(1/9.8) ≈ 2.0 s.

Work = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J.

A plane mirror always produces a virtual and erect image, which is the same size as the object.