A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, pointing into the paper as shown below. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed vis: ←→ L X BLv(x/R) B²L²v(x/R) B²L²V/R BLv No force (zero Newton)

The current in a long, straight conductor has the following form:I(t) = I0cos ωtWhat is the magnitude of the magnetic field a distance r away from theconductor?

Diamagnets have the property that they "dampen" the effects of an external magnetic field by creating an opposing magnetic field. The diamagnet thus has an induced dipole moment that is anti- aligned, such that the induced north pole is closer to the north pole creating the external field. An application of this is that diamagnets can be levitated 2. Now, the mathematics of generally describing a force by a non-uniform field on a dipole is a little beyond the scope of this course, but we can still work through an approximation based on energy. Essentially, whenever the theoretical loss of gravitational potential energy from "falling" no longer can "pay the cost" of increasing the magnetic potential energy, the object no longer wants to fall. Suppose a diamagnetic object floats above the levitator where the magnitude of the magnetic field is 12 T, which is inducing" a magnetic dipole moment of 4.6 LA - m² in the object. The magnetic field 1.9 mm below the object is stronger with a…

A cube of edge length e = 6.0 cm is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components B, = +7.0 T, B, = +2.0 T, and B, = +7.0 T. (a) Calculate the flux through the shaded face of the cube. T•m2 (b) What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)? T•m²

Two conducting plates are in parallel and carry net charge of opposite signs with the same magnitude. A particle with negative charge -q is sent into the region between the plates with speed v as shown. What must be the direction of the uniformn magnetic field in the space between the plates such that -q passes in between the plates with no deflections?

A current I is passed through a wire. A second wire of length L is moving perpendicular to the magnetic field generated by the first wire (see sketch below) with velocity v at a distance d. Write down the expression for the potential difference V between the ends of the moving wire. Consider the magnetic field B to be constant over the range of motion of the second wire (i.e. d » 1). Use μ for the vacuum permittivity. Please use appropriate algebraic symbols for multiplication (* for a × b), division (/ for a/b), exponents (a^b for a³), square root (sqrt(a*b/c) for √a× b/c) etc. For Greek letters use their names e.g. "theta", "alpha", "pi", "mu" (without the quotes) and for trigonometric functions use "cos", "tan", "sin" (without the quotes). Thus for Acose use A*cos theta. Please use the "Display response" button to check you entered the answer you expect. Wire 1 Wire 2 d V

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