Exam 29: Magnetic Fields

A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in a direction that makes an angle of 37° above the positive x axis in the xy plane. At the instant it enters a magnetic field of (5.0 ) mT it experiences an acceleration of (8.0 ) m/s². What is the charge of the particle?

A charged particle (mass = 4.0 μg, charge = 5.0 μC) moves in a region where the only force on it is magnetic. What is the magnitude of the acceleration of the particle at a point where the speed of the particle is 5.0 km/s, the magnitude of the magnetic field is 8.0 mT, and the angle between the direction of the magnetic field and the velocity of the particle is 60°?

An electron moves in a region where the magnetic field is uniform, has a magnitude of 60 μT, and points in the positive x direction. At t = 0 the electron has a velocity that has an x component of 30 km/s, a y component of 40 km/s, and a z component of zero. What is the pitch of the resulting helical path?

A particle (q = 5.0 nC, m = 3.0 μg) moves in a region where the magnetic field has components B_x = 2.0 mT, B_y = 3.0 mT, and B_z = −4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle?

A 2.0-C charge moves with a velocity of ( ) m/s and experiences a magnetic force of ( ) N. The x component of the magnetic field is equal to zero. Determine the y component of the magnetic field.

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

The boundary shown is that of a uniform magnetic field directed in the positive z direction. An electron enters the magnetic field with a velocity pointing along the x axis and exits 0.63 μs later at point A. What is the magnitude of the magnetic field?

A proton is accelerated from rest through a potential difference of 2.5 kV and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path?

A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with a speed V?

An electron has a velocity of 6.0 × 10⁶ m/s in the positive x direction at a point where the magnetic field has the components B_x = 3.0 T, B_y = 1.5 T, and B_z = 2.0 T. What is the magnitude of the acceleration of the electron at this point?

A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20°. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it.

Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.40 T) with speeds of 5 000 km/s follow circular paths that differ in diameter by 5.0 cm. What is the difference in the mass of these two ions?

A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with speed V?

Three particles of equal charge, X, Y, and Z, enter a uniform magnetic field B. X has velocity of magnitude v parallel to the field. Y has velocity of magnitude v perpendicular to the field. Z has equal velocity components v parallel and perpendicular to the field. Rank the radii of their orbits from least to greatest.

At what speed would a proton need to circle the Earth at a height of 1 000 km above the equator if the Earth's magnetic field is horizontal and directed north-south, with an intensity of 4.00 × 10−⁸ T? (The radius of the Earth is 6 400 km and the charge and mass of the proton are q = 1.60 × 10−¹⁹ C and m_p = 1.67 × 10−²⁷ kg. Ignore relativistic corrections.)

What is the magnitude of the magnetic force on a charged particle (Q = 5.0 μC) moving with a speed of 80 km/s in the positive x direction at a point where B_x = 5.0 T, B_y = −4.0 T, and B_z = 3.0 T?

A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits?

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

A proton with a kinetic energy of 0.20 keV follows a circular path in a region where the magnetic field is uniform and has a magnitude of 60 mT. What is the radius of this path?

A physicist claims that she has found a new particle with a mass 200 000 times the mass of the proton (1.67 × 10−²⁷ kg) and a charge of 3.20 × 10−¹⁹ C. If she is correct, such a particle traveling in a circle in a uniform 5.00 T magnetic field at a velocity of 2 500 m/s will have a radius of