A circular area with a radius of 6.50 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.230 T at an angle of 53.1° from the +z-direction?

A flat, square surface with side length $3.40\mathrm{cm}$ is in the xy-plane at $z=0$. Calculate the magnitude of the flux through this surface produced by a magnetic field $B=\left(0.200T\right)i+\left(0.300T\right)j-\left(0.500T\right)k$.

An open plastic soda bottle with an opening diameter of 2.5 cm is placed on a table. A uniform 1.75 T magnetic field directed upward and oriented 25° from vertical encompasses the bottle. What is the total magnetic flux through the plastic of the soda bottle?

A 150 g ball containing 4.00 x 10⁸ excess electrons is dropped into a 125 m vertical shaft. At the bottom of the shaft, the ball suddenly enters a uniform horizontal magnetic field that has magnitude 0.250 T and direction from east to west. If air resistance is negligibly small, find the magnitude and direction of the force that this magnetic field exerts on the ball just as it enters the field.

A particle with mass $1.81\times {10}^{-3}$ $\mathrm{kg}$ and a charge of $1.22\times {10}^{-8}\text{ C}$ has, at a given instant, a velocity $v=(3.00\times {10}^4\text{ m/s})j$. What are the magnitude and direction of the particle's acceleration produced by a uniform magnetic field $B=\left(1.63T\right)i+\left(0.980T\right)j$?

A horizontal rectangular surface has dimensions 2.80 cm by 3.20 cm and is in a uniform magnetic field that is directed at an angle of 30.0° above the horizontal. What must the magnitude of the magnetic field be to produce a flux of 3.10 x 10^-4 Wb through the surface?

An electron experiences a magnetic force of magnitude 4.60 x10^-15 N when moving at an angle of 60.0° with respect to a magnetic field of magnitude 3.50 x 10^-3 T. Find the speed of the electron.