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 wires are parallel and carry current in opposite directions. The currents are 8.0 A and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point midway between the wires is:

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:

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

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 outside the shell (r > R_o). 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:

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

Suitable units for $\mu$ ₀ are:

A "coulomb" is:

If the radius of a pair of Helmholtz coils is R then the distance between the coils is:

A square loop of current-carrying wire with edge length a is in the xy plane, the origin being at its center. Along which of the following lines can a charge move without experiencing a magnetic force?

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

Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in opposite directions. The force per unit length in N/m of one wire on the other 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:

A toroid has a square cross section with the length of an edge equal to the radius of the inner surface. The ratio of the magnitude of the magnetic field at the inner surface to the magnitude of the field at the outer surface is:

A constant current is sent through a helical coil. The coil:

Two long ideal solenoids (with radii 20 mm and 30 mm respectively) carry the have the same number of turnes of wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. It is observed that there is zero magnetic field within the inner solenoid is zero. The current in the inner solenoid must be:

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:

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.

Helmholtz coils are commonly used in the laboratory because the magnetic field between them: