Question

A loop ABCDEFA of straight edges has six corner points A (0,0,0), B (5,0,0), C (5,5,0), D (0,5,0), E (0,5,5) and F (0,0,5). The magnetic field in this region is \[\overrightarrow B = \left( {3\widehat i + 4\widehat {k}} \right)T\]. The quantity of flux through the loop ABCDEFA (in Wb) is ______.

Answer 1

Hint: The number of magnetic field lines passing through the given closed surface is called Magnetic flux. It is denoted by $\phi $ and the unit is Weber. The magnetic flux indicates the strength of magnetic lines that are produced by a magnet.

Complete step by step solution:

Given six corners are A (0,0,0), B (5,0,0), C (5,5,0), D (0,5,0), E (0,5,5) and F (0,0,5).
The Magnetic field, \[\overrightarrow B = \left( {3\widehat i + 4\widehat k} \right)T\]
The Magnetic flux =?
We know that magnetic flux is given by the formula, $\phi = \overrightarrow B .\overrightarrow A $
Then \[\overrightarrow A = \] (Area of ABCD) $\left( {\widehat k} \right)$+ (Area of ADEF) \[\left( {\widehat i} \right)\]
\[ \Rightarrow \overrightarrow A = 25\widehat k + 25\widehat i\]
Substituting the values of $\overrightarrow A $ and $\overrightarrow B $, we get,
\[\Rightarrow \phi = \left( {3\widehat i + 4\widehat k} \right)\left( {25\widehat i + 25\widehat k} \right)\]
\[\Rightarrow \phi = 75 + 100 = 175\]
$\therefore \phi = 175Wb$

Thus the quantity of flux through the loop ABCDEFA is 175 Wb.

Additional Information:
1. A closed path in a circuit is called a loop. It is used for executing a set of statements repeatedly, till a particular condition is satisfied.
2. Within the human body, the low-frequency magnetic fields induce the circulating currents.

Note: 1. Magnetic flux starts from the north pole and ends at the south pole and they will never intersect each other. The lines of forces that are parallel to each other and in the same direction will repel each other.
2. The magnetic flux in the open surface is not zero and through a closed surface is zero always. It always forms a closed loop. The magnetic flux depends on the area and the magnetic strength of the magnet.
3. The region around a magnet where the moving charge experiences a force is called a magnetic field. It depends on the magnet.