Magnetic Field

To solve the problem, we need to calculate the force per unit length on wire ‘A’ after wire ‘B’ is removed, given the initial condition that the net force per unit length on wire ‘C’ was when all three wires were present.

1. Understanding the Magnetic Force Between Two Parallel Currents:
The magnetic force per unit length between two parallel wires carrying currents and separated by a distance is given by:

- The force is attractive if the currents are in the same direction.
- The force is repulsive if the currents are in opposite directions.

2. Interpreting the Diagram and Currents:
From the diagram:
- Wire A carries current (upward),
- Wire B carries current (downward),
- Wire C carries current (upward),
- Each wire is separated by a distance .

3. Initial Force on Wire ‘C’:
The net force per unit length on wire C, due to A and B, is given as .

4. Force on Wire ‘A’ When Wire ‘B’ is Removed:
Now, we are to calculate the force on wire A when only wire C is present along with it, i.e., wire B is removed.

- Wire A and C both carry current in the same direction (upward), and are separated by .
- The force between them is attractive.
So, the force per unit length on A due to C is:

5. Analyzing the Given Information:
Previously, when all three wires were present, the net force on wire C was due to A and B.
Let us use symmetry and force directions to note that in the original configuration, wire B’s presence reduced the total force between A and C, as B’s current was in the opposite direction.
Removing B increases the force (because now A feels full attractive force from C alone).
The change in net force is found to be triple the original and in the opposite direction.

Final Answer:
The new force per unit length on wire A is .

To solve the problem, we need to determine the angle between a current element and the position vector of a point at which the magnetic field is zero.

1. Understanding the Magnetic Field due to a Current Element:
According to the Biot-Savart Law, the magnetic field at a point due to a current element is given by:

Where:
- is the vector length element in the direction of current,
- is the position vector from the current element to the point of interest,
- is the magnetic field at that point.

2. Cross Product Implication:
The magnetic field is determined by the cross product .
If the angle between and is or , the sine of the angle is zero:
and
Therefore, the magnitude of the magnetic field becomes zero at that point.

3. Condition for Zero Magnetic Field:
For the cross product to be zero, the two vectors must be parallel or anti-parallel, i.e., the angle must be or .

Final Answer:
The angle between the current element and the position vector must be or for the magnetic field to be zero at that point.

To solve the problem, we need to relate the magnetic susceptibility and the relative permeability for a ferromagnetic substance.

1. Understanding the Relationship:
For any magnetic material, the relationship between relative permeability and magnetic susceptibility is given by:

2. Behavior of Ferromagnetic Materials:
Ferromagnetic substances have a very high value of susceptibility , which means they are strongly magnetized in the presence of a magnetic field.
Therefore, for ferromagnetic substances:

So,

3. Eliminating Incorrect Options:
- Option 1: → Incorrect (this is true for diamagnetic or weak paramagnetic materials)
- Option 2: → Incorrect (this is never true for ferromagnetic materials)
- Option 3: → Incorrect (this would imply the material does not respond to magnetic field)
- Option 4: → Correct

Final Answer:
For ferromagnetic materials, .

Step 1: The formula for the maximum induced emf in a rotating coil in a magnetic field is given by: where: - (number of turns) - (magnetic field) - (area of the coil) - (angular speed)

Step 2: Substituting the values into the equation: Thus, the maximum emf induced in the coil is .