Exam 29: Magnetic Fields Due to Currents

Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1.The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is:

Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown.At what value of x is the net magnetic field zero?

The magnetic field at any point in the xy plane is given by , where is the position vector of the point, A is a constant, and is a unit vector in the +z direction.The net current through a circle of radius R, in the xy plane and centered at the origin is given by:

Lines of the magnetic field produced by a long straight wire carrying a current are:

The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r)and radial lengths.The circuits carry the same current.Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest.

The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated.Rank the arrangements according to the magnitudes of the magnetic fields at the midpoints between the loops on the central axes, from least to greatest.

In Ampere's law, , the integration must be over any:

Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown below.They each carry 2.0 A, out of the paper.The magnetic field at the third vertex (P)has magnitude:

In Ampere's law, the direction of the integration around the path:

A toroid with a square cross section carries current i.The magnetic field has its largest magnitude:

Two parallel long wires carry the same current and repel each other with a force F per unit length.If both these currents are doubled and the wire separation tripled, the force per unit length becomes:

A long straight cylindrical shell has an inner radius R_i and an outer radius R_o.It carries a current i, uniformly distributed over its cross section.A wire is parallel to the cylinder axis, in the hollow region (r < R_i).The magnetic field is zero everywhere in the hollow region.We conclude that the wire:

In the figure, the current element , the point P, and the three vectors (1, 2, 3)are all in the plane of the page.The direction of , due to this current element, at the point P is:

Suitable units for $\mu$ ₀ are:

The magnitude of the magnetic field at point P, at the center of the semicircle shown, is given by:

The magnetic field outside a long straight current-carrying wire depends on the distance R from the wire axis according to:

A semi-infinite wire runs along the positive y axis, beginning at the origin (x = y = 0)and extending infinitely far in the +y direction.If the current in the wire is 12 A, what magnetic field does it create on the x axis at the point x = 3.5 cm?

In an overhead straight wire, the current is north.The magnetic field due to this current, at our point of observation, is:

Two long parallel straight wires carry equal currents in opposite directions.At a point midway between the wires, the magnetic field they produce is:

Four long straight wires carry equal currents into the page as shown.The magnetic force exerted on wire F is: