Just pretend that the cases are numbered 1-5

Yes,

NO,

Yes,

Yes,

No.

Explanation:

CASE: A wire is moved through the field of a magnet

As the wire is moved through the field of a magnetic the magnetic flux through the circuit loop changes,; therefore current is induced.

CASE: A magnet is held close to a wire

There needs to be relative motion between the wire and the magnet for the current to be induced; therefore, simply holding a magnet close to a wire will not induce current in the circuit.

CASE: A magnet is moved into a coil of wire

As the magnet is moved into a coil of wire, the magnetic flux through the coil changes, and therefore, the current is induced.

CASE: A magnet is moved out of  coil of wire

Moving a magnet out of  coil of wire also changes the magnetic flux through the coil; therefore, the current is induced.

CASE: A magnet rests in coil of wire

There needs to be relative motion between the coil of wire and the magnet for the current to be induced; therefore, a magnet resting in the coil of wire will no induce any current in the coil.

a charge 3q is at the origin, and a charge −2q is on the positive x axis at x=a. part a where on the x-axis would you place a third charge so it would experience no net electric force? enter an expression for the exact answer, which will involve a square-root sign. (do not enter an approximate decimal answer.)

3. dark matter

empty space could also be a simple vacuum