Question

relating electric current and magnetic fields
which statements are true about moving the compass around the wire? check all that apply.
with no current, the compass needle will not move.
if the light bulb is on, the compass needle will move.
if the circuit is on, compass needle movement will indicate a dead battery.
if current is flowing, the compass needle will not move unless the compass is touching the wire.
changing the battery terminals will change the current flow and the compass will point differently.

Explanation:

• When there is no current (\(I = 0\)), there is no magnetic field produced by the wire (from \(B=\mu_0\frac{I}{2\pi r}\), where \(B\) is the magnetic - field, \(\mu_0\) is the permeability of free space, \(I\) is current, and \(r\) is the distance from the wire). So, the compass needle (which aligns with magnetic fields) will not move.
• If the light - bulb is on, there is a current in the circuit. A current - carrying wire produces a magnetic field (\(B=\mu_0\frac{I}{2\pi r}

eq0\)), and this magnetic field will interact with the compass needle (due to the force on a magnetic dipole in a magnetic field \( \vec{\tau}=\vec{\mu}\times\vec{B}\), where \(\vec{\tau}\) is the torque, \(\vec{\mu}\) is the magnetic dipole moment of the compass needle, and \(\vec{B}\) is the magnetic field from the wire), causing it to move.

• If the circuit is on (\(I

eq0\)), the compass - needle movement indicates the presence of a magnetic field due to the current, not a dead battery. A dead battery would mean \(I = 0\) (no current).

• If current is flowing (\(I

eq0\)), the magnetic field \(B=\mu_0\frac{I}{2\pi r}\) exists at points around the wire (not just when \(r = 0\), i.e., not just when the compass is touching the wire). The compass needle will move as long as it is in the vicinity of the current - carrying wire (non - zero \(B\) at non - zero \(r\)).

• Changing the battery terminals reverses the current direction (\(I\to - I\)). Using the right - hand rule (for the direction of the magnetic field around a current - carrying wire: if the current direction changes, the direction of the magnetic field \(B\) (given by \(\vec{B}=\frac{\mu_0}{4\pi}\frac{I\vec{dl}\times\hat{r}}{r^{2}}\)) changes. Since the compass needle aligns with the magnetic field, it will point differently.

Answer:

• With no current, the compass needle will not move.
• If the light bulb is on, the compass needle will move.
• Changing the battery terminals will change the current flow and the compass will point differently.