You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

More about Magnetic Dipoles

A circular lo...

Question

A circular loop carrying a current i is made of a wire of length L. A uniform magnetic field B exists parallel to the plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger?

Open in App

Solution

Given,
Magnetic field intensity = B
Circumference, L = 2πr, where r is the radius of the coil.
So, area of the coil, A $= \frac{L^{2}}{4 π}$
Magnitude of current = i
Torque acting on the coil,
τ = niABsinθ, where θ is the angle between the area vector and the magnetic field.
$τ = n i A B = \frac{i L^{2} B}{4 π}$
(b) Let s be the length of the square loop.
$4 s = L \Rightarrow s = \frac{L}{4} A = {(\frac{L}{4})}^{2} = (\frac{L^{2}}{16}) τ = n i A B = \frac{i L^{2} B}{16}$
So, the torque on the circular loop is larger.

Suggest Corrections

Similar questions

Q. A loop is formed by joining two semicircular wires of radii

R_{1}

and

R_{2}

carrying a current as shown in the figure. The current in the loop is

I

and is placed in the uniform magnetic field

B

which is parallel to the plane of loop. What will be the torque acting on the loop.

Q. A loop

P Q R

carries a current of

2 A

as shown. A uniform magnetic field

(B = 2 T)

is parallel to plane of the loop. The magnetic torque on the loop is:

Q. A wire loop formed by joining two semicircular wires of radii

R_{1}

and

R_{2}

carries a current as shown in the adjoining diagram. The current in the loop is

I

and it is placed in a uniform magnetic field

B

, parallel to its plane. What will be the torque acting on the loop?

Q. A circular loop of wire having a radius of

8.0 cm

carries a current of

0.2 A

. A vector of unit length and parallel to the dipole moment

\to μ

of the loop is given by

0.60^i - 0.80^j

. If the loop is located in uniform magnetic field given by

\to B = (0.25)^i + (0.30)^k

. Find the torque acting on the loop.

A wire of length l, carrying current is bent into a loop and placed with its plane perpendicular to a magnetic field. In which of the following shapes, is the torque acting on the loop maximum?

Join BYJU'S Learning Program