Suppose that you have an electron moving with speed comparable to the speed of light in a circular orbit of radius r in a large region of uniform magnetic field B. Now the uniform magnetic field begins to increase with time: $B=B_{0}+b t,$ where $B_{0}$ and b are positive constants. In one orbit, how much does the energy of the electron increase, assuming that in one orbit the radius doesn't change very much?

If the magnetic field in a particular pulse has a magnitude of $1 \times 10^{-5}\ \mathrm{T}$ (comparable to the Earth's magnetic field), what is the magnitude of the associated electric field?

Which term best describes this collection of locations: a forest, a freshwater lake, an estuary, and a prairie? A. ecosystem diversity, B. extinction, C. genetic diversity, D. species diversity.

Crayon companies recommend treating wax stains on clothes by spraying the stains with an oily lubricant, applying dish washing liquid, and then washing the clothes. Explain in a paragraph why this treatment would remove the stain.

What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?

Write a sentence explaining its significance to electing leaders. platform

Which actions by humans have affected the following groups of marine animals: giant clams, snails, sharks, sea turtles, seabirds?

Evaluate the matrix products.

$$\left( \begin{array} { l l l } { 1 } & { 1 } & { 1 } \\ { 0 } & { 1 } & { 1 } \\ { 0 } & { 0 } & { 1 } \end{array} \right) \left( \begin{array} { l l l } { 1 } & { 1 } & { 1 } \\ { 0 } & { 1 } & { 1 } \\ { 0 } & { 0 } & { 1 } \end{array} \right)$$

The magnetic field in a solenoid is $B=\mu_{0} N I / d .$ A circular wire of radius 10 cm is concentric with a solenoid of radius 2 cm and length d = 1 m, containing 10,000 turns. The current increases at a rate of 50 A/s. What is the non-Coulomb electric field in the wire?

A thick wire of radius R carries a constant current I. Find the magnetic field inside the wire, a distance r from the center of the wire and far from the ends of the wire, where r < R and R is much less than the length of the wire.

The center of a thin paper cube in outer space is located at the origin. Each edge is 10 cm long. The only other objects in the neighborhood are some small charged particles whose charges and positions at this instant are the following: +9 nC at $\langle 4,2,-3\rangle\ \mathrm{cm},$ -6 nC at $\langle 1,-3,2\rangle\ \mathrm{cm},$ +7 nC at $\langle 15,0,4\rangle\ \mathrm{cm},$ + 4 nC at $\langle- 1,3,2\rangle\ \mathrm{cm},$ and -3 nC at $\langle- 2,12,-3\rangle\ \mathrm{cm} .$ The electric flux on five of the six faces of the cube totals $564 \mathrm{V} \cdot \mathrm{m} .$ What is the flux on the other face?

NASA has recently launched space probes to explore Mars. Why might Mars have been chosen for these explorations?

What type of spectrum is produced when the light emitted directly from a hot, low-density cloud of gas passes through a prism?

Vector u has a magnitude of 3 and an angle of $30^{\circ}$ from the positive x-axis. How many unique vectors in the same plane with the same initial point as u have a magnitude of 2 and are perpendicular to u? List them.