Two long parallel conductors \(S_1\) and \(S_2\) are separated by a distance \(10\) cm and carrying currents of \(4\) A and \(2\) A respectively. The conductors are placed along x-axis in X–Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of \(3π\) coulomb is passing through the point P with velocity \(\overrightarrow v=(2\hat i+3\hat j)\) m/s; where \(\hat i\) and \(\hat j\) represents unit vector along x & y axis respectively. The force acting on the charge particle is \(4π×10^{−5}(−x\hat i+2\hat j)N\). The value of x is:
Two long parallel conductors \(S_1\) and \(S_2\) are separated by a distance \(10\) cm and carrying currents of \(4\) A and \(2\) A respectively. The conductors are placed along x-axis in X–Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of \(3π\) coulomb is passing through the point P with velocity \(\overrightarrow v=(2\hat i+3\hat j)\) m/s; where \(\hat i\) and \(\hat j\) represents unit vector along x & y axis respectively. The force acting on the charge particle is \(4π×10^{−5}(−x\hat i+2\hat j)N\). The value of x is:
- 2
- 1
- 3
- -3
The Correct Option is C
Solution and Explanation
Field at P is
=\(\bigg(\frac{µ_0×i_1}{2πr_1}–\frac{µ_0i_2}{2πr_2}\bigg)\bigg(−\hat k\bigg)\)
=\(−\bigg(\frac{µ_04}{2π×0.04}−\frac{µ_0×2}{2π×0.06}\bigg)\hat k=–\frac{µ_0×200}{6π}\hat k\)
Therefore, the force
\(\overrightarrow F=\overrightarrow {qv} ×\overrightarrow B\)
= \(3π(2\hat i+3\hat j)×\bigg(−\bigg(\frac{µ_0×200}{6π}\bigg)\hat k\bigg)\)
=\(3π\bigg(\frac{200µ_0}{3π\hat j}−\frac{100µ_0}{π}\hat i)\)
= \(200µ_0\hat j–300µ_0\hat i\)
= \(4π×10^{−5}(2\hat j–3\hat i)\)
\(Hence,\) \(x = 3\)
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Concepts Used:
Semiconductors
Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.
Properties of Semiconductor:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.