A single turn current loop in the shape of a right angle triangle with sides 5cm, 12cm, 13cm is carrying a current of 2A. The loop is in a uniform magnetic field of magnitude 0.75T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be \(\frac{x}{130} N\). The value of x is ________ .
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For magnetic forces on a current-carrying wire, use F = ILB sinθ. Ensure L and B are in consistent units.
Correct Answer: 9
Approach Solution - 1
The force on a straight conductor in a magnetic field is given by:
\[ F = I L B \sin \theta \]
Here:
- \(I = 2 \, \text{A},\)
- \(L = 5 \, \text{cm} = 0.05 \, \text{m},\)
- \(B = 0.75 \, \text{T},\)
- \(\sin \theta = 1\) (since \(B\) is perpendicular to the 5 cm side).
Substitute the values:
\[ F = (2)(0.05)(0.75)(1) = 0.075 \, \text{N} \]
The force is given as \(\frac{x}{130} \, \text{N}\). Equating:
\[ \frac{x}{130} = 0.075 \implies x = 0.075 \cdot 130 = 9.75 \]
Thus, the value of \(x\) is 9.
Approach Solution -2
Force on 5cm side is
∣F∣= ILB sinθ
=(2)(5×10−2)×43×1312=1309N
So, x=9
Hence, The correct answer is 9.
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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.