Magnetic field at the centre of a circular coil of radius R carrying current 'i' is B\proptot/R and its direction is given by R. right-hand thumb rule. Magnetic field at the centre of acircular arc subtending an angle θ B\proptoi/R(\theta/360^\circ) and its direction can be found using right hand rule Consider two circular coils made of uniform conductors as shown in figure 3 and 4. In figure 3 points C and D are diametrically opposite to each other and in figure 4 \anglePO_2Q=120^\circ.Then magnetic fields_____________.

Correct Answer is : At both O1 and O2 are zero.

At both O_1 and O_2 are non-zero.

At zero at O_1 but non-zero at O_2

Is non-zero at O_1 but zero at O_2

NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 71 of 100

Marks: +1, -0

Magnetic field at the centre of a circular coil of radius R carrying current 'i' is

B∝t/R

and its direction is given by R. right-hand thumb rule. Magnetic field at the centre of acircular arc subtending an angle θ

B∝i/R(θ/360°)

and its direction can be found using right hand rule

Consider two circular coils made of uniform conductors as shown in figure 3 and 4. In figure 3 points C and D are diametrically opposite to each other and in figure 4

∠PO_2Q=120°

.Then magnetic fields_____________.

At both $O_1$ and $O_2$ are zero.
At both $O_1$ and $O_2$ are non-zero.
At zero at $O_1$ but non-zero at $O_2$
Is non-zero at $O_1$ but zero at O_2

Validate

Solution:

According to the figure 3,

B∝i/R[/360°]

So, according to figure 3,

i_1=i[{πR_2}/{2πR}]=i/4

i_2=i[{{3πR}/2}/{2πR}]=3/4i

Given that

B∝i/R[θ/360°]

So,

B_1=Ki_1/R[270°/360°]

[into to plane]

B_2=Ki_2/R[90°/360°]

[out of the plane]
where,

2i_1=33i_1

Now,

B_1/B_2={Ki_1R}/{R.Ki_2}[270°/360°][360°/90°]

⇒B_1/B_2=1

So, net field at

O_1

is zero
Similarly, from figure 4

i_4=2i_3

and

B_3={Ki_3}/R[240°/360°]

[into the plane]

B_4={Ki_4}/R[120°/360°]

[out of the plane]
Now,

B_3/B_4=1

So net field

O_2

is zero.

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