Magnets and Magnetic Fields Practice Problems

A proton projected into a region of a uniform magnetic field of magnitude 4.20 × 10^-3 T is subjected to a magnetic force of magnitude 5.00 × 10^-15 N. The angle between the proton's velocity and the direction of the magnetic field is 45.0°. What is the proton speed?

The center of mass of a rectangular sheet of dimension a = 4.50 cm and b = 3.50 cm is placed on the horizontal plane at the origin O. In this region, the magnetic field is 1.50î + 2.00ĵ - 3.00k̂. What is the magnitude of the magnetic flux through the sheet?

The mass of alpha particles is 6.64 × 10^-27 Kg and their charge is 3.20 × 10^-19 C. An alpha particle emitted by a radioactive substance moves into a region of uniform magnetic field given by B = (2.0 0T)î + (3.20 T)ĵ. At a given moment, the alpha particle has a velocity v = (12.00 × 10⁴ m/s)î. Find the i) magnitude (a) and ii) direction of its acceleration vector at this particular moment.

A velocity selector in a mass spectrometer uses a 0.150 T magnetic field and a 0.31 × 10⁴ V/m electric field. The fields are uniform and perpendicular to one another. Doubly ionized gold ions (Au²⁺) of mass m pass through the velocity selector zone with an initial velocity perpendicular to both electric and magnetic fields. i) Determine the speed of the particles that pass through the velocity selector zone without being deflected by the fields. Then Au²⁺ particles pass through a region of a transverse magnetic field, where they travel in a circular trajectory with a radius of 14.0 cm. ii) Determine the mass of Au²⁺.

A small brass sphere of mass 12.0 g has 3.00 × 10⁷ excess electrons. The sphere is released without initial speed from the top of a tower. At 100 m below the release point, the sphere encounters a magnetic field of strength 1.18 T directed toward the east. Determine the strength and direction of the force exerted on the sphere by the magnetic field. Neglect air resistance

A source generates a uniform magnetic field of strength 1.15 T that is directed at an angle of 37.0° from the z-direction. A water pitcher made of glass with a circular plastic top lid of 7.00 cm radius lies, within the magnetic field, on the top of a horizontal table. Determine the total magnetic flux passing through the pitcher glass.

A square coil with side l = 4.0 cm is placed in a 0.45 T magnetic field. The plane of the coil makes an angle of 35.0° with the field lines. The magnetic flux Φ_B passing through the coil is 2.05 × 10^-4 Wb. Determine the magnetic field's strength that generates this flux.

A round loop with a radius of 15.0 cm is placed on a horizontal table. A solenoid produces a uniform magnetic field of strength 0.32 T. The magnetic field is directed at an angle of 42.0° below the horizontal. Determine the magnitude of the magnetic flux through the loop.

The brain is modeled as a current loop in its outer layers, with a 14 cm diameter loop. Consider the magnetoencephalography (MEG) experiment, where the magnetic field at the center of the brain is measured to be 1000 fT for one loop. What is the magnitude of the brain's magnetic dipole moment?

Bohr's model proposes that the angular momentum of an electron is quantized in multiples of ℏ (h-bar). For an electron going around and around in a circular path in a 1.2 T magnetic field, what are the allowed radii for i) n = 1 and ii) n = 2?

A beam of electrons (charge e = -1.60 × 10^-19 C, mass 9.11 × 10^-31 kg) is accelerated from rest through a potential difference of 2.0 kV and enters the region between two parallel metal plates perpendicular to the electric field. The plates have an area of 35.0 cm² and are separated by 5.0 mm, with a 200-V battery connected across them. To make sure the beam of electrons is undeflected from between the plates, a magnetic field is applied perpendicular to the electric field between the plates. Determine the magnitude and direction of the magnetic field.