Magnetic Field Produced by Straight Currents Practice Problems

Static magnetic fields result from the flow of direct current in electric power transmission systems. A researcher studying the hazards of magnetic fields placed a tesla meter 15.0 meters below a transmission line crossing the university campus. i) What will be the reading on the tesla meter if the transmission line carries a steady current of 100.0 A. ii) Determine the ratio of the measured magnetic field to the earth's magnetic field at the university campus which is 50 μT.

A current-carrying wire is placed as depicted in the figure below. Determine the magnetic field vectors at points X, Y, and Z. Provide your answers as vectors, indicating both magnitude and direction.

Three infinitely long wires are placed at the vertices of a virtual equiangular triangle with a side length of 4.5 cm. The triangle lies in the plane of the page, and the wires are perpendicular to the page. Two of the wires carry a current of 3.0 A out of the page, while the third wire carries a current of 3.0 A into the page. Calculate the magnetic field strength at the triangle's centroid.

Lead is a metal that exhibits superconductivity below a critical temperature of 7.2 K. However, if the magnetic field at the surface of a lead wire exceeds 0.15 T, the superconductivity is lost. Determine the maximum current that can flow through a straight lead wire with a radius of 2.5 mm.

If the magnetic field along the central axis measures 300 μT at a separation of 8.00 cm from a small bar magnet, determine the field strength along the central axis at a separation of 12.0 cm from the same bar magnet.

Identify the locations on the x-axis where the magnetic field is zero when there is a setup involving a long wire with a 7.0 A current intersecting the x-axis at x = -3.0 cm and another parallel wire with a 4.0 A current intersecting the x-axis at x = +3.0 cm? Consider both scenarios: (i) when the currents flow in the same direction, and (ii) when the currents flow in opposite directions.

The diagram below shows a rail gun that can launch a metal projectile. The projectile has a mass of 20 g and rests on two horizontal rails that are 1.5 m long and connected to a 500 V power supply. A magnetic field of 0.08 T acts between the rails. The rails have a resistivity of 0.15 Ω/m. The switch is closed when the projectile is in the middle of the rails. Ignore friction and resistance at the contacts, and assume the projectile has no electrical resistance. Find the speed of the projectile when it leaves the rails.

A hybrid car is equipped with a high-voltage battery that supplies a current of 50.0 A to a 1.5 cm diameter parallel-plate capacitor. If a sensor is placed 3.0 mm radially from the center of the capacitor, what would it register as the magnetic field strength?

A square loop with side lengths of 12.0 cm, a mass of 50 g, and a resistance of 0.030 Ω, is 75% submerged in a magnetic field. The plane of the loop is perpendicular to the field. At t=0 s, the magnetic field strength is suddenly increased from 0.6 T to 1.6 T over a span of 0.025 s. Calculate the speed at which the loop is driven away from the field. Remember that only the part of the loop within the magnetic field will experience the effects of the field change.

An electric train uses a cable that carries an electric current of about 150 A when it is operating at full capacity. What will be the strength of the magnetic field that is generated by this cable at a distance of 3 m? Compare it with Earth's Magnetic Field which is 5 x 10⁻⁵ T.

Determine the magnitude of the induced magnetic field from a continuous stream of electrons passing through space with an intensity of 5×10¹³ electrons/second at a point located 0.8 meters away from the stream.

In a laboratory demonstration, two long parallel wires, each 50 m long, are kept 5.0 cm apart. Both wires carry a current of 40 A in the same direction. Calculate the magnitude and direction of the forces on them.