A uniform current carrying cylindrical wire carries current \(I\) having radius 'a'. Magnetic field with distance x varies with relation given:
- B ∝ x, for x < a
B ∝\(\frac{1}{x}\), for x > a - B ∝ x, for x < a
B is constant, for x > a - B is constant, for x < a
B ∝\(\frac{1}{x}\), for x > a - B ∝\(\frac{1}{x}\), for x < a
B ∝ x, for x > a
The Correct Option is A
Solution and Explanation
B is directly proportional to ‘x’, for when the ‘x’ is lesser than ‘a’
The B is inversely proportional to ‘x’, for when the ‘x’ is greater than ‘a’.
So, the correct option is (A)
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.