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MHT CET 202624 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
24 April
Shift
Morning Shift
Subject
Physics
Chapter
Magnetic Effects of Current

MHT CET 2026 · 24 April · Morning Shift · Physics · Magnetic Effects of Current

If the current 'i' is passing through the wire, it has a shape as...

If the current 'i' is passing through the wire, it has a shape as shown in the figure. The radius of the curved part is R and the linear part is assumed to be very long. The magnetic induction of the field at the point O, is
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Options

  1. Aμ0i2πR\lleft(2+π2)\dfrac{\mu_0 i}{2\pi R} \l left(2+\dfrac{\pi}{2})
  2. Bμ0i4πR\l(2+π)\dfrac{\mu_0 i}{4\pi R} \l\left(2+\pi\right)
  3. Cμ0i2πR\lleft(1+3π2)\dfrac{\mu_0 i}{2\pi R} \l left(1+\dfrac{3\pi}{2})
  4. Dμ0iπR\lleft(1+π2)\dfrac{\mu_0 i}{\pi R} \l left(1+\dfrac{\pi}{2})

Correct answer

B. μ0i4πR\l(2+π)\dfrac{\mu_0 i}{4\pi R} \l\left(2+\pi\right)

Step-by-step solution

The wire can be divided into three parts: a lower semi-infinite straight wire, a semicircular arc, and an upper semi-infinite straight wire.

The magnetic field at point O due to the lower semi-infinite straight wire is given by B1=μ0i4πRB_1 = \dfrac{\mu_0 i}{4\pi R}. Applying the right-hand rule, the current is towards the left and point O is above the wire, so the magnetic field is directed into the page.

The magnetic field at point O due to the semicircular arc is given by B2=μ0i4R=πμ0i4πRB_2 = \dfrac{\mu_0 i}{4R} = \dfrac{\pi \mu_0 i}{4\pi R}. The current is in the clockwise direction, so the magnetic field is directed into the page.

The magnetic field at point O due to the upper semi-infinite straight wire is given by B3=μ0i4πRB_3 = \dfrac{\mu_0 i}{4\pi R}. The current is towards the right and point O is below the wire, so the magnetic field is directed into the page.

Since all three magnetic field components are in the same direction, the total magnetic field at O is their sum:

Bnet=B1+B2+B3B_{net} = B_1 + B_2 + B_3

Bnet=μ0i4πR+πμ0i4πR+μ0i4πRB_{net} = \dfrac{\mu_0 i}{4\pi R} + \dfrac{\pi \mu_0 i}{4\pi R} + \dfrac{\mu_0 i}{4\pi R}

Bnet=μ0i4πR(1+π+1)B_{net} = \dfrac{\mu_0 i}{4\pi R}(1 + \pi + 1)

Bnet=μ0i4πR(2+π)B_{net} = \dfrac{\mu_0 i}{4\pi R}(2 + \pi)
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