CameraIcon

SearchIcon

MyQuestionIcon

179

You visited us 179 times! Enjoying our articles? Unlock Full Access!

Magnetic Field Due to Current Carrying Circular Loop

Two semicircl...

Question

Two semicircles are shown in the figure having radius $R_{1}$ and $R_{2}$ , carrying current $I_{1}$ and $I_{2}$ respectively. Find the ratio $\frac{I_{1}}{I_{2}}$ so that the net magnetic field at the centre is zero.
(Assume that straight wire segments pass through the centre.)

A

\frac{R_{1}}{R_{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\sqrt{\frac{R_{1}}{R_{2}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

{(\frac{R_{1}}{R_{2}})}^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

{(\frac{R_{1}}{R_{2}})}^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{R_{1}}{R_{2}}$

We know that, magnetic field due to a semi-circular loop at the centre is given by,

$B_{O} = \frac{μ_{o} I}{4 r}$

As the net magnetic field at the centre is zero, so,

$\frac{μ_{o} I_{1}}{4 R_{1}} = \frac{μ_{o} I_{2}}{4 R_{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{R_{1}}{R_{2}}$

Why this question?
The magnetic field due to a semi-circular loop at the centre is given by, $B = \frac{μ_{o} I}{4 a}$ .

Suggest Corrections

thumbs-up

3

Similar questions

Q. Two concentric co-planar circular loops of radii

r_{1}

r_{2}

carry currents of respectively

i_{1}

i_{2}

in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of loops is half that due to

i_{1}

alone at the centre. If

r_{2} = 2 r_{1}

i_{2} / i_{1}

Q. A circular loop of radius

R

carries current

I_{2}

in a clockwise direction, as shown in the figure. The centre of the loop is at a distance

D

above a long straight wire. What should be the magnitude and direction of the current

I_{1}

in the straight wire so that the net magnetic field at the centre of the loop is zero?

Q. Assertion :The magnetic field at the centre of the circular coil in the following figure due to the currents

I_{1}

I_{2}

is zero, Reason:

I_{1} = I_{2}

implies that the fields due to the current

I_{1}

I_{2}

will be balanced.

Q. Two concentric circular loops of radii

r_{1}

r_{2}

carry clockwise and anticlockwise currents

i_{1}

i_{2}

. If the the centre is a null point, then

i_{1}

i_{2}

Q. The magnitude of gravitation field intensities at distance

r_{1}

r_{2}

from the centre of a uniform solid sphere of radius

R

M

I_{1}

I_{2}

respectively. Find the ratio of

I_{1} / I_{2}

r_{1} > R

r_{2} > R

r_{1} < R

r_{2} < R

r_{1} > R

r_{2} < R

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Magnetic Field Due to Current Carrying Circular Loop

Standard X Physics

Join BYJU'S Learning Program

CrossIcon