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1. What is meant by the net longitudinal differential of the components of a vector field?
2. Give an example in which the net longitudinal differential of the components of a vec- tor is zero, although the individual derivatives are nonzero.
3. What is the expansion for the divergence of a vector?
4. State Gauss' law for the magnetic field in differential form. How is it derived from its integral form?
A charging RC circuit controls the intermittent windshield wipers in a car. The emf is 12.0 V. What resistance should be used in the charging circuit
A moving particle encounters an external electric field that decreases its kinetic energy from 9710 eV to 8150 eV as the particle moves from position A to position B. Determine the charge of the particle
A bomb at rest at the origin of an xy-coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, what is the magnitude of the velocity of the third piece
You throw a 20-N rock vertically into the air from ground level. You observe that when it is a height 15.4m above the ground, Use the work-energy theorem to find its maximum height
hanging wire has a length of 1.90m . when a steel ball of mass 51.0 kg is suspended from the wire the wire stretches by
An undersea research chamber is spherical with an external diameterof 4.90 m. The mass of the chamber, when occupied, is61300 kg. What is the buoyant force on the chamber
a magnetic field has a magnitude of 1.20 x 10-3 t and an electric field has a magnitude of 4.70 x 103 nc. both fields
A 1300 kg truck drives around a flat 230 m -diameter circular race course at 27 m/s. What is the magnitude of the net force on the car
A 10.0 g object moving to the right at 15.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 34.0 cm/s
A mica sheet 1.14 µm thick is suspended in air. In reflected light, there are gaps in the visible spectrum at 428, 535, and 642 nm. Compute the index of refraction of the mica sheet.
A 2 kg mass dropped 2.0 m above a spring with a spring constant of 40.0 N/m. How much does the spring compress
During a lightning flash, there exists a potential difference of V(Cloud)-V(Ground)=1.2 x10^9V between a cloud and the ground. As a result, a charge of -25 C is transferred from the ground to the cloud.
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