Correct Answer - Option 4 : independent of shape of the wire
CONCEPT:
- The flow of current in a conductor is due to the motion of free electrons in a definite direction.
- When such a conductor is placed in a magnetic field, each electron moving in the uniform magnetic field experiences a force in a specific direction.
- The direction of this force is given by fleming's left-hand rule.
- Let us take a conductor of uniform cross-section A and length l. Let the number density of mobile charge carriers (electron, in this case) be n. So total mobile no of mobile charge carriers will be nlA.
- In presence of an external magnetic field, force in these charge carriers is given by
\(⇒ \overrightarrow{F}= nlAq \overrightarrow{v_{d}}× \overrightarrow{B}\)
Where q is the charge and B is the external magnetic field, |nqvd|A is the current I flowing through the conductor.
- Magnetic force in a current-carrying conductor is given by
\(⇒ \overrightarrow{F}= I \overrightarrow{l}× \overrightarrow{B}\)
Where \(\vec{F}\) is the magnetic force, \(\vec{B}\) is the magnetic field, \(\vec{l}\)is the length of the conductor, and I is the current flowing through the conductor, and θ is the angle between the length of the conductor (in direction of current flow) and magnetic field.
EXPLANATION:
- Magnetic force in a current-carrying conductor is given by
\(\Rightarrow F = Il B\sin \theta \)
- The magnetic force depends upon:
- length of the current-carrying conductor
- current in the conductor
- magnetic field
- the angle between the magnetic field and the length of the current element.
- So the magnetic force is independent of the shape of the wire. Hence option 4 is correct.