Exam 23: Electric Potential

Mass spectrometer: In a mass spectrometer, a singly-charged particle (charge e) has a speed of 1.0 × 10⁶ m/s and enters a uniform magnetic field of 0.20 T. The radius of the circular orbit of the particle is 0.020 m. What is the mass of this particle? (e = 1.60 × 10^-19C)

Toroids: A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A. What is the magnitude of the magnetic field inside the solenoid at the central radius? (μ₀ = 4π × 10^-7 T ∙ m/A)

Field of a long wire: Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure. The wires pass through the vertices of a right isosceles triangle of side 2.00 cm. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle?

Field due to a long wire: The figure shows two long wires carrying equal currents I₁ and I₂ flowing in opposite directions. Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire?

Field of a long wire: Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ₀ = 4π × 10^-7 T ∙ m/A)

Velocity selector: A proton, with mass 1.67 × 10^-27 kg and charge +1.6 × 10^-19 C, is sent with velocity 7.1 × 10⁴ m/s in the +x direction into a region where there is a uniform electric field of magnitude 730 V/m in the +y direction. What are the magnitude and direction of the uniform magnetic field in the region, if the proton is to pass through undeflected? Assume that the magnetic field has no x-component and neglect gravitational effects.

Force on parallel wires: The figure shows three long, parallel, current-carrying wires. The current directions are indicated for currents I₁ and I₃. The arrow labeled F represents the net magnetic force acting on current I₃. The three currents have equal magnitudes. What is the direction of the current I₂?

Velocity selector: A beam of electrons is accelerated through a potential difference of 10 kV before entering a region having uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the direction in which the electron is moving. If the magnetic field in this region has a value of 0.010 T, what magnitude of the electric field is required if the particles are to be undeflected as they pass through the region?

Force on currents: A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire?

Circular motion of charges: As shown in the figure, a small particle of charge q = - 7.0 × C and mass has velocity as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R = 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region.

Field of a long wire: A very long thin wire produces a magnetic field of at a distance of from the central axis of the wire. What is the magnitude of the current in the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

Solenoids: A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N? (μ₀ = 4π × 10^-7 T ∙ m/A)

Field due to a long wire: Two very long parallel wires are a distance d apart and carry equal currents in opposite directions. The locations where the net magnetic field due to these currents is equal to zero are

Field of a long wire: Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the magnitude of the magnetic field midway between the two wires? (μ₀ = 4π × 10^-7 T ∙ m/A)

Ampere's law: A coaxial cable consists of an inner cylindrical conductor of radius R₁ = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R₂ = 0.080 m and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ₀ = 4π × 10^-7 T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable)

Force on moving charges: An electron moving in the direction of the +x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, the direction of the magnetic field in this region points in the direction of the

Field of a circular loop: A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 10⁶ m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10^-19 C, μ₀ = 4π × 10^-7 T ∙ m/A)

Torque: A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil?

Potential energy of a current loop: A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A ∙ m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. The work done by this external torque is closest to

Force on currents: A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod?