Question

If a conductor of length 1 m carrying a current of 2 A is placed in a field of 0.2 T. What will be the force acting on it?

Hint:

If a problem gives $I, L, B$ and asks for force without specifying an angle, always assume perpendicular placement ($\theta = 90^\circ$) to find the maximum standard force.

Answer 1

Step 1: Understanding the Concept:
When a current-carrying conductor is placed in an external magnetic field, it experiences a magnetic force. This is the fundamental principle behind electric motors.
Step 2: Key Formula or Approach:
The magnitude of the magnetic force on a straight current-carrying conductor is given by the formula:
\[ F = I L B \sin(\theta) \]
Where:
\(F\) = Magnetic force
\(I\) = Current
\(L\) = Length of the conductor in the field
\(B\) = Magnetic field strength
\(\theta\) = Angle between the direction of current and the magnetic field.
When the angle is not explicitly specified in such problems, standard practice is to assume maximum force, meaning the conductor is placed perpendicular to the field (\(\theta = 90^\circ\), \(\sin 90^\circ = 1\)).
Step 3: Detailed Explanation:
Given values:
Length, \(L = 1\) m
Current, \(I = 2\) A
Magnetic field, \(B = 0.2\) T
Assuming perpendicular orientation (\(\theta = 90^\circ\)):
\[ F = I \times L \times B \times \sin(90^\circ) \]
\[ F = 2 \times 1 \times 0.2 \times 1 \]
\[ F = 0.4 \text{ Newtons} \]
Step 4: Final Answer:
The force acting on the conductor is 0.4 N.