A small immersion heater is rated at 285 W . The specific heat of water is 4186 J/kg⋅C∘. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 20 ∘C to 64 ∘C. Ignore the heat loss to the surrounding environment.

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants

In a classical model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius 0.053 nm. what is the electron's orbital frequency? what is the effective current of the electron?