(a) the net force and torque on the coil are both zero.
(b) the net force is zero but torque is finite.
(c) the net force is finite but torque is zero.
(d) the net force and torque are both finite.
Answer: (a) the net force and torque on the coil are both
zero.
Explanation:
CONCEPT
- When
a current-carrying conductor is placed in a magnetic
field, it experiences a magnetic force.
- In
a current-carrying coil, each segment of the
coil experiences a force.
- The
behavior of the coil depends on:
- Field
uniformity
- Orientation
of the coil with respect to the magnetic field
Force Acting on the Circular Coil
- The
force on a current-carrying conductor is given by:
Where:
= current in the
conductor
= effective
length of the conductor
= magnetic field
strength
= angle between
the conductor (or plane of the coil) and the magnetic field
- In a
circular coil:
- The left
and right sides experience forces that are:
- Equal
in magnitude
- Opposite
in direction
- Along
the same line of action
- These
forces cancel each other.
Net Force on the Coil
- Since
all forces cancel pairwise:
- Therefore, for
any current-carrying coil placed in a uniform magnetic field, the net
force is always zero.
Torque on the Coil
- The
torque acting on a current-carrying coil is given by:
Or in vector form:
Where:
= number of turns
= area of the
coil
= magnetic moment
vector (normal to the coil)
= magnetic
induction vector
Given Orientation
- The
coil is placed in the direction of magnetic induction.
- This
means:
- The plane
of the coil is perpendicular to the magnetic field
- The normal
to the coil is parallel to the magnetic field
- Hence,
the angle between and is:
Resulting Torque
- Since:
- The
torque becomes:
FINAL CONCLUSION
- For
a current-carrying loop placed in a uniform magnetic field:
- Net
force on the loop is zero
- Torque
depends on orientation
- In
the given orientation (coil aligned with the magnetic field):
- Net
force = 0
- Torque
= 0
Correct Answer
✅ Option (a): Net force
on the loop is zero
✔️ Key One-Line Exam Statement
A current-carrying loop in a uniform magnetic field
experiences zero net force; torque depends on its orientation.