A rectilinear homogeneous conductor OA of mass 12 g and of length 36cm hangs freely from its upper end O while its lower end A slightly touches the surface of the mercury. Terminals C and D are connected to a generator which supplies a current 7.4A. A horizontal magnetic field is made to act on a part of the wire. The direction of B is directed towards the reader , it is observed that conductor OA is shifted from its vertical position of equilibrium by an angle 5º30' .
Precise the polarity of terminals C and D.
Thx
To determine the polarity of terminals C and D, we need to consider the direction of the current flowing through the conductor OA and the direction of the magnetic field.
Let's break down the given information:
- The conductor OA hangs freely, meaning there is no external force acting on it.
- The lower end A touches the surface of the mercury, implying that there is a current passing through the conductor.
- The current passing through OA is 7.4A, and the direction of the magnetic field (B) is directed towards the reader.
- The conductor OA is shifted from its vertical position of equilibrium by an angle of 5º30'.
Now, let's analyze the situation step by step:
Step 1: Determine the direction of the magnetic force
The magnetic force acting on a current-carrying conductor in a magnetic field is given by the right-hand rule. According to the right-hand rule, if you point your thumb in the direction of the current and curl your fingers in the direction of the magnetic field, the direction your palm faces will indicate the direction of the magnetic force.
In this case, the current is flowing from terminal C to terminal D. Since we know that the magnetic field (B) is directed towards the reader, we can use the right-hand rule to determine the direction of the magnetic force acting on conductor OA.
Using the right-hand rule, we find that the magnetic force points towards the left.
Step 2: Analyze the equilibrium position
The conductor OA is shifted from its vertical position of equilibrium by an angle of 5º30'. This means that there must be an external force acting on the conductor in the opposite direction of the magnetic force in order to create the observed displacement.
Since the conductor is homogeneously charged, the net force acting on it must be zero in the vertical direction for it to remain in equilibrium. Therefore, there must be an upward force that is equal in magnitude and opposite in direction to the downward force exerted by the magnetic force.
Step 3: Determine the polarity of terminals C and D
Knowing the above information, we can determine the polarity of terminals C and D.
- The force exerted by the magnetic field is directed towards the left.
- To counteract this force and maintain equilibrium, an upward force is required.
- According to the right-hand rule, the upward force is produced by an electric field, which means there must be a potential difference across the conductor.
- Since the lower end A of the conductor touches the surface of the mercury, it implies that there is a current flowing through the conductor from terminal C to terminal D.
Based on the above information, we can conclude that terminal C is positive, and terminal D is negative.
Therefore, the polarity of terminals C and D is as follows:
- Terminal C: positive
- Terminal D: negative
To determine the polarity of terminals C and D, we need to consider the relationship between the angle of displacement and the direction of the magnetic field.
Given information:
- The conductor OA is a rectilinear homogeneous conductor.
- The conductor has a mass of 12 g and a length of 36 cm.
- The conductor hangs freely from its upper end O, and its lower end A slightly touches the surface of the mercury.
- Terminals C and D are connected to a generator supplying a current of 7.4 A.
- A horizontal magnetic field is applied perpendicular to the conductor, directed towards the reader.
- The conductor OA is shifted from its vertical position of equilibrium by an angle of 5º30' (5 degrees and 30 minutes).
To determine the polarity, we need to analyze the relationship between the current direction, magnetic field direction, and the resultant force acting on the conductor.
First, let's determine the direction of the current flow in the conductor. It is mentioned that terminals C and D are connected to a generator. However, the question does not provide any specific information about the direction of the current. Therefore, we cannot precisely determine the direction of the current flowing in the conductor from the given information. You may need to refer to additional information or assumptions to determine the current direction.
Next, let's consider the resultant force acting on the conductor. When a current-carrying conductor is placed in a magnetic field, a force is exerted on it, known as the magnetic force or the Lorentz force. This force can cause the conductor to move or experience a torque.
Since the conductor is hanging freely, we can assume that the angle of displacement observed (5º30') is due to the torque acting on the conductor.
The torque acting on the conductor is given by the equation τ = F * d * sinθ, where F is the magnetic force, d is the perpendicular distance between the conductor and the point of application of the force, and θ is the angle between the force and the direction of the magnetic field.
In this case, the angle of displacement (5º30') is due to the torque. The direction of displacement indicates the direction of the torque, which will be perpendicular to both the magnetic field and the current direction.
Considering the conductor is shifted towards the reader, this suggests that the torque is acting in a counterclockwise direction. Therefore, the magnetic force on the conductor must be directed upwards.
Now, let's relate the direction of the magnetic force with the polarity of terminals C and D. The direction of the magnetic force on a current-carrying conductor depends on the right-hand rule. According to the right-hand rule, if we place our right hand with the thumb pointing in the direction of the current and the fingers pointing in the direction of the magnetic field, the palm of the hand will face the direction of the magnetic force.
Since the conductor is shifted towards the reader, the magnetic force acting on the conductor will be directed upwards. Therefore, the polarity of the terminals C and D should be such that the terminal C should be positive, and the terminal D should be negative. This ensures that the current flows from C to D, creating an upward magnetic force on the conductor.
In conclusion, based on the given information and the observed displacement of the conductor OA, the polarity of terminals C and D should be as follows: Terminal C should be positive (+), and terminal D should be negative (-). Please note that the current direction was assumed, and if you have any additional information or assumptions about the current direction, it should be taken into consideration.