The current of 5 A flows in a square loop of sides 1 m placed in air. The magnetic field at the center of the loop is \(X\sqrt{2} \times 10^{-7} \, T\). The value of X = _________.
Correct Answer: 40
Solution and Explanation
The magnetic field B is given by:
\[ B = 4 \times \frac{\mu_0 I}{4 \pi \left(\frac{1}{2}\right)} \left( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \right). \]
Substituting the values:
\[ B = 4 \times \frac{10^{-7} \times 5}{\frac{\pi}{2}} \left( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \right). \]
Simplifying:
\[ B = 4 \times \frac{10^{-7} \times 5 \times 2}{\pi} \times \frac{2}{\sqrt{2}}. \]
Further simplifying:
\[ B = 4 \times 10^{-7} \times 5 \times 2 \times \sqrt{2}. \]
\[ B = 40 \sqrt{2} \times 10^{-7} \, \text{T}. \]
Final Answer:
\[ B = 40 \sqrt{2} \times 10^{-7} \, \text{T}. \]
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Concepts Used:
Magnetic Force
Magnetic force is the attraction or repulsion force that results from the motion of electrically charged particles. The magnets are attracted or repellent to one another due to this force. A compass, a motor, the magnets that hold the refrigerator door, train tracks, and modern roller coasters are all examples of magnetic power.
A magnetic field is generated by all moving charges, and the charges that pass through its regions feel a force. Depending on whether the force is attractive or repulsive, it may be positive or negative. The magnetism force is determined by the object's charge, velocity, and magnetic field.
Read More: Magnetic Force and Magnetic Field
The magnitude of the magnetic force depends on how much charge is in how much motion in each of the objects and how far apart they are.
Mathematically, we can write magnetic force as:
A charge will feel a force as it passes through a magnetic field at an angle. This force is given by the equation:
A force acts on the motion of charge q traveling with velocity v in a Magnetism field, and this force is:
- Perpendicular to both v and B.
- Perpendicular to sinθ (where θ is the angle between v and B).
- Proportional to the charge q.
- Proportional to the velocity v.