Force on Moving Charges & Right Hand Rule Practice Problems

A helium nucleus, composed of two protons and two neutrons, is in motion within a magnetic field B = 1.25 k T. Its velocity is measured at 2.0 × 10⁷ m/s, as shown in the figure below. For every situation outlined, calculate the magnetic force, denoted as F, exerted on this helium nucleus. Please present your solution in terms of its components.

A conducting rod with a mass of m lies in the middle of two frictionless conducting rods. The two rods have a separation of x. The uniform magnetic field (of magnitude B) in that region points downward. Should the current in the conducting rod flow in a direction from P to Q or from Q to P in order for the rod to roll to the left? 

A group of astrophysicists researching the Van Allen radiation belts surrounding the Earth have identified electromagnetic radiation at a frequency of 60 MHz. They theorize that this radiation is a result of electrons spiraling within the Earth's magnetic field. Determine the strength of the magnetic field in the area where these radiation belts are located.

You are given a cyclotron to distinguish two ions with very similar masses. The magnetic field used has a strength of 2.8000 T. Masses of extra or deficient electrons are assumed negligible when using 5 significant figures. The ions CO₂⁺ and C₃H₈⁺ have a nominal molecular mass of 44. Use the atomic masses of the molecules as 44.010 u and 44.096 u, respectively, to calculate the cyclotron frequencies of the ions. Take 1 u = 1.6605 × 10^-27 kg and e = 1.6022 × 10^-19 C.

Consider a particle accelerator that moves particles along a circular path with a diameter of 72 cm. The accelerator uses a potential difference of 300 V, which reverses its direction after every half cycle. If the accelerator uses a magnetic field of 1.6 T, determine the maximum kinetic energy achieved by an alpha particle moving along this circular trajectory.

Work out the magnitude and direction of the total force experienced by the alpha particle in the image below. Specify direction as a clockwise or counterclockwise angle from the horizontal. 

Imagine that a beta particle, which has the same mass and charge as an electron, enters a specific region as shown in the image below. This region has both electric and magnetic fields within it. Calculate what the magnitude and direction of this particular particle's acceleration will be at the exact moment depicted in the diagram.

A proton is shot into a uniform 6.50 T magnetic field as shown below. The magnetic field is directed in the negative z-direction. The proton's velocity is 3.25 × 10⁷ m/s directed at 28.5 degrees above the xy plane. The proton moves in a spiral trajectory inside the magnetic field. Calculate the pitch and radius of the trajectory. 

An alpha particle passes undeflected through a region with both electric and magnetic fields. This means that the net force on the particle is zero. An observer in the frame of the alpha particle would see the alpha particle stationary. How does the observer explain why the force on the alpha particle is zero?

A proton with a velocity v = 3.6 × 10⁶ ĵ m/s is shot into an electric field E = (3.0 × 10⁵ î + 3.0 × 10⁵ ĵ) V/m, and B = 0.20 k̂ T. Determine the total force experienced by the proton.

Two alpha particles move perpendicular to each other at velocities: v_a = 3.2 × 10 ⁶ î m/s and v_b = 2.5 × 10 ⁶ ĵ m/s. The alpha particles enter a region with a uniform magnetic field. Both particles will experience magnetic forces of magnitude of: F_a = 1.6 × 10 ^-15 k̂ N and F_b = -1.8 × 10 ^-15 k̂ N, respectively, while remaining within the same magnetic field. Calculate what the magnetic field's strength and direction will be given as a counterclockwise angle from the +x-axis. Also assume that v_a points along the +x-axis.

A proton in a particle accelerator is speeded up using a potential difference of 8 kV and then sent into a 3.0 cm wide space containing a uniform magnetic field. If the proton experiences a deflection of 15° due to the magnetic field, calculate the magnitude of the magnetic field.

A neutron moves at a speed of 2.3 × 10⁶ m/s in the negative x-direction past a stationary observer on Earth. An electron is launched relative to the same stationary observer with a speed v = (2.7 × 10⁶ i + 2.7 × 10⁶j) m/s. Calculate the electron's speed and direction measured from the y-axis as observed by the neutron.

In an experimental setup, protons are accelerated using a 75 kV potential difference. After acceleration, they pass through a uniform magnetic field B. This magnetic field deflects the protons sideways, causing them to hit a detector positioned 25 cm horizontally and 13 cm vertically from their original path. Determine the approximate value of magnetic field B to the nearest tenth. [Hint: Mass of proton = 1836 times the mass of the electron, m_e = 9.109 × 10^-31 kg, Charge of proton = 1.602 × 10^-19 C]

An electron is part of a research experiment in a physics lab. As it travels vertically to the north, it is accelerated to a speed of 8.50 × 10⁵ m/s. The lab's magnetic field generator creates a field of 0.75 T directed horizontally to the east. Determine the magnitude and direction of the force experienced by the electron due to the magnetic field.

In a 0.660 T magnetic field directed horizontally away from the observer, an electron is projected upward at 2.50 × 10⁶ m/s. What will be its path in this field?

What magnetic field strength is necessary to bend protons (charge q = +e, mass m = 1.67 x 10⁻²⁷ kg) moving at 2.2 x 10⁶ m/s into a circular path with a radius of 0.20 m?

A proton (charge = +1.6 × 10^-19 C) is in a magnetic field given by B̅ = (0.20 î + 0.40 ĵ) T. The velocity with which it is moving in the field is represented by v̅ = (3.0 î - 2.0 ĵ) × 10⁶ m/s. What is the magnitude and the direction of the force experienced by the proton?

An electron with a velocity of 3.0 × 10⁶ m/s moves through a uniform magnetic field of 1.00 × 10^-9 T perpendicular to its direction of motion. If the electron has a charge of -1.6 × 10^-19 C, how far will it be deflected from its path after it has traveled 0.50 km? Ignore relativistic effects.