Understanding Maximum Force on Current-Carrying Conductor
The force experienced by a current-carrying conductor placed in a magnetic field is governed by the Lorentz force law.
The magnitude of this force ($F$) is given by the formula:
$F = BIL \sin(\theta)$
Where:
- $B$ is the magnetic field strength
- $I$ is the current flowing through the conductor
- $L$ is the length of the conductor within the magnetic field
- $\theta$ is the angle between the direction of the current ($I$) and the direction of the magnetic field ($B$)
To find when the force is maximum, we need to consider the term $\sin(\theta)$ in the formula. The sine function has a maximum value of 1.
- The maximum value of $\sin(\theta)$ is 1, which occurs when $\theta = 90^{\circ}$.
- This means the force ($F$) is maximum when the angle between the current and the magnetic field is $90^{\circ}$.
Therefore, the force on a current-carrying conductor in a magnetic field is maximum when the current is perpendicular to the magnetic field.
Conversely, the force is minimum (zero) when $\sin(\theta) = 0$, which occurs when $\theta = 0^{\circ}$ (current parallel to the field) or $\theta = 180^{\circ}$ (current anti-parallel to the field).
Important Questions from Magnetic Force on a Current-Carrying Wire
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Consider the following image:
A proton enters a magnetic field at right angles to it, as shown above. The direction of force acting on the proton will be
Consider the following statements about a solenoid:
1. The magnetic field strength in a solenoid depends upon the number of turns per unit length in the solenoid
2. The magnetic field strength in a solenoid depends upon the current flowing in the wire of the solenoid
3. The magnetic field strength in a solenoid depends upon the diameter of the solenoid
Which of the statements given above are correct?
