Ampere's Law — Prelims Questions

A long straight wire of radius $R$ carries a steady current $I$ uniformly distributed over its cross-section. Which of the following graphs correctly represents the variation of magnetic field $B$ with distance $r$ from the center of the wire?

A long solenoid has 1000 turns per meter and carries a current of $5,\text{A}$. What is the magnetic field inside the solenoid?

An Amperian loop encloses two parallel wires. Wire 1 carries a current of $3,\text{A}$ out of the page, and Wire 2 carries a current of $5,\text{A}$ into the page. If the Amperian loop is traversed clockwise (when viewed from above), what is the net current enclosed ($I_{enc}$)?

Which of the following statements about Ampere's Law is INCORRECT?

A toroid has a total of $N$ turns and carries a current $I$. The inner radius is $R_1$ and the outer radius is $R_2$. What is the magnetic field at a point inside the toroid at a radial distance $r$ such that $R_1 < r < R_2$?

A coaxial cable consists of an inner solid conductor of radius $a$ carrying current $I$ and a thin outer cylindrical shell of radius $b$ carrying current $I$ in the opposite direction. What is the magnetic field in the region between the inner conductor and the outer shell ($a < r < b$)?

A very long cylindrical conductor of radius $R$ has a cylindrical hole of radius $a$ bored through its entire length. The axis of the hole is parallel to the axis of the conductor and is at a distance $d$ from it. The conductor carries a uniform current density $J$. What is the magnetic field at the center of the hole?