Exam 29: The Magnetic Field

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

A long, straight wire with current flowing through it produces magnetic field strength at its surface. If the wire has a radius R, where within the wire is the field strength equal to of the field strength at the surface of the wire? Assume that the current density is uniform throughout the wire. (μ₀ = 4π × 10^-7 T ∙ m/A)

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.

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?

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. (a) What is the current in the loop? (b) Find the magnitude of the magnetic torque exerted on the loop. (c) If the loop is released from rest, in what direction will points a and c initially move?

A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field. (a) What is the magnitude of the magnetic moment of the loop? (b) What torque does the magnetic field exert on the loop?

The figure shows three long, parallel current-carrying wires. The magnitudes of the currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?

A wire segment 1.2 m long carries a current I = 3.5 A, and is oriented as shown in the figure. The +x-axis points directly into the page. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. What is the magnetic force vector on the wire segment?

A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long. The windings carry a current I in the sense that is shown in the figure. The current produces a magnetic field, of magnitude near the center of the solenoid. Find the current in the solenoid windings.

A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm. A uniform current density of 1.0 A/ cm² flows through the cylinder parallel to its axis. Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder. (μ₀ = 4π × 10^-7 T ∙ m/A)

A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction. A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown. Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop. What is the magnetic field vector at point P due to these two currents? (μ₀ = 4π × 10^-7 T ∙ m/A)

A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field. (a) Which way should the magnetic field point? (b) What is the magnitude of the weakest possible magnetic field you could use?

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)

Two circular coils of diameter 30.0 cm are parallel to each other and have their centers along the same line L but separated by 22.0 cm. When an experimenter views the coils along L, the coil closer to her carries a clockwise current of 2.50 A. Find the magnitude and sense (clockwise or counterclockwise) of the current needed in the other coil so that the net magnetic field on L midway between the two coils will have a magnitude of 4.10 µT and point away from the experimenter who is viewing the coils along L. (μ₀ = 4π × 10^-7 T ∙ m/A)

As shown in the figure, two long straight wires are separated by a distance of The currents are to the right in the upper wire and to the left in the lower wire. What are the magnitude and direction of the magnetic field at point P, which is a distance below the lower wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

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.

As shown in the figure, a rectangular current loop is carrying current = 3.0 A, in the direction shown, and is located near a long wire carrying a current . The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire, as shown. We measure that the net force on the rectangular loop is and is directed towards the wire. (μ₀ = 4π × 10^-7 T ∙ m/A) (a) What is the magnitude of the current I_w? (b) In which direction does I_w flow: from top to bottom or from bottom to top in the sketch?

A rectangular loop of wire measures 1.0 m by 1.0 cm. If a 7.0-A current flows through the wire, what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ₀ = 4π × 10^-7 T ∙ m/A)

An electron moving with a velocity = 5.0 × 10⁷ m/s enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is = . What magnetic field will allow the electron to go through the region without being deflected?