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University Physics Volume 2

Challenge Problems

University Physics Volume 2Challenge Problems

Challenge Problems

89.

The accompanying figure shows a flat, infinitely long sheet of width a that carries a current I uniformly distributed across it. Find the magnetic field at the point P, which is in the plane of the sheet and at a distance x from one edge. Test your result for the limit a→0.a→0.

This picture shows a flat, infinitely long sheet of width a that carries a current I uniformly distributed across it. Point P is in the plane of the sheet and at a distance x from one edge.
90.

A hypothetical current flowing in the z-direction creates the field B→=C[(x/y2)i^+(1/y)j^]B→=C[(x/y2)i^+(1/y)j^] in the rectangular region of the xy-plane shown in the accompanying figure. Use Ampère’s law to find the current through the rectangle.

This figure shows the rectangular region of the xy-plane; z axis is perpendicular to the plane. Points a1 and a2 are located at the x axis. Points b1 and b2 are located at the y axis. There is an equal distance between all points.
91.

A nonconducting hard rubber circular disk of radius R is painted with a uniform surface charge density σ.σ. It is rotated about its axis with angular speed ω.ω. (a) Find the magnetic field produced at a point on the axis a distance h meters from the center of the disk. (b) Find the numerical value of magnitude of the magnetic field when σ=1C/m2,σ=1C/m2, R=20 cm,h=2 cm,R=20 cm,h=2 cm, and ω=400rad/sec,ω=400rad/sec, and compare it with the magnitude of magnetic field of Earth, which is about 1/2 Gauss.

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