Answer
64.8k+ views
Hint: The current carrying conductor experiences a force when it is placed in an external magnetic field. If equal force is applied on the ends of a current carrying conductor separated by a distance, there is rotation caused in the current carrying conductor due to a quantity called torque.
Complete step by step solution:
When a current carrying conductor is placed in an external magnetic field, a force is applied on the conductor equal to,
$F = BIL\sin \theta $
where,
B = magnetic field
I = current in the conductor
L = length of the conductor
$\theta $ = relative angle between the direction of magnetic field and the current carrying conductor.
If we consider a loop carrying conductor, this equal force acting on the loop about its centroid, causes a rotational effect on the loop, which is measured by the quantity called torque.
Torque is the product of magnitude of force and the distance of separation between the points where force is applied.
If we consider a loop of area A with current flowing I and placed in a magnetic field B, the torque acting on the loop is given by the formula –
$\tau = IAB$
where I = current, A = area of loop, B = magnetic field.
Consider a triangle loop of length $l$ carrying current $i$ with the direction of magnetic field B as follows:
![](https://www.vedantu.com/question-sets/d6cba74d-b7a2-44c3-b140-b27f508a4aa37363397553192726426.png)
The area of the triangle is given by the formula –
$\Rightarrow A = \dfrac{{\sqrt 3 }}{4}{l^2}$
The torque acting on the loop is given by –
$\Rightarrow \tau = iAB$
Substituting the value of area A in the above expression , we have –
$\Rightarrow \tau = \dfrac{{\sqrt 3 }}{4}iB{l^2}$
Hence, the correct option is Option C.
Note: In this problem, the triangular loop has only one turn. The torque on the loop is directly proportional to the number of turns in the loop. Hence, torque acting on a loop with N number of turns is given by –
$\tau = NIAB$.
Complete step by step solution:
When a current carrying conductor is placed in an external magnetic field, a force is applied on the conductor equal to,
$F = BIL\sin \theta $
where,
B = magnetic field
I = current in the conductor
L = length of the conductor
$\theta $ = relative angle between the direction of magnetic field and the current carrying conductor.
If we consider a loop carrying conductor, this equal force acting on the loop about its centroid, causes a rotational effect on the loop, which is measured by the quantity called torque.
Torque is the product of magnitude of force and the distance of separation between the points where force is applied.
If we consider a loop of area A with current flowing I and placed in a magnetic field B, the torque acting on the loop is given by the formula –
$\tau = IAB$
where I = current, A = area of loop, B = magnetic field.
Consider a triangle loop of length $l$ carrying current $i$ with the direction of magnetic field B as follows:
![](https://www.vedantu.com/question-sets/d6cba74d-b7a2-44c3-b140-b27f508a4aa37363397553192726426.png)
The area of the triangle is given by the formula –
$\Rightarrow A = \dfrac{{\sqrt 3 }}{4}{l^2}$
The torque acting on the loop is given by –
$\Rightarrow \tau = iAB$
Substituting the value of area A in the above expression , we have –
$\Rightarrow \tau = \dfrac{{\sqrt 3 }}{4}iB{l^2}$
Hence, the correct option is Option C.
Note: In this problem, the triangular loop has only one turn. The torque on the loop is directly proportional to the number of turns in the loop. Hence, torque acting on a loop with N number of turns is given by –
$\tau = NIAB$.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)