Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires
- $\frac{\mu_0 i}{2 r}\left(1+\frac{1}{\pi}\right)$
- $\frac{\mu_0 i}{2 r}\left(1+\frac{2}{\pi}\right)$
- $\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{\pi}\right)$
- $\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$
The Correct Option is D
Solution and Explanation
Applying Biot-Savart’s Law: \[ B_p = \left( \frac{\mu_0 I}{4r} + \frac{\mu_0 I}{4\pi r} \right) = \frac{\mu_0 I}{2r} \left( \frac{1}{2} + \frac{1}{2\pi} \right) \]
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter