Question

A charge q is placed at (1,2,1) and another charge -q is placed at (0,1,0) such that they form an electric dipole . There exists a uniform electric field E=2icap. calculate the torque experienced by the dipole
(answer is 2√2q N-m)​

Answer 1

Answer:

$\tau = 2\sqrt2 q$

Explanation:

As we know that dipole moment of the dipole is given as

$\vec P = q\vec a$

here we know that

$\vec a = r_+ - r_-$

$\vec a = (1\hat i + 2\hat j + 1\hat k) - (0\hat i + 1\hat j + 0\hat k)$

$\vec a = 1\hat i + 1\hat j + 1\hat k$

now we know that

$\vec P = q(1\hat i + 1\hat j + 1\hat k)$

now torque due to electric field on dipole is given as

$\tau = \vec P \times \vec E$

$\tau = q(1\hat i + 1\hat j + 1\hat k) \times (2\hat i)$

$\tau = q(-2\hat k + 2\hat j)$

$\tau = 2\sqrt2 q$

#Learn

Topic : Torque on dipole in uniform electric field

https://brainly.in/question/8041957

Answer 2

The torque is $2\sqrt{2q}\ N-m$

Explanation:

Given that,

Position of charge $r_{1}= (1,2,1)$

Position  of charge $r_{2}=(0,1,0)$

Electric field $E= 2i$

We need to calculate the force

Using formula of electric field

$E= \dfrac{F}{q}$

$F=Eq$

Put the value into the formula

$F=2i q$

We need to calculate the distance

Using formula of distance

$r_{21}=r_{2}-r_{1}$

Put the value into the formula

$r_{21}=0i+j+0k-i-2j-k$

$r_{21}=-i-j-k$

We need to calculate the torque

Using force of torque

$\tau=F\times r$

Put the value into the formula

$\tau=2i q\times(-i-j-k)$

$\tau=(2j-2k)q$

The magnitude of the torque is

$|\tau|=\sqrt{(2^2+2^2)q}$

$|\tau|=2\sqrt{2q}\ N-m$

Hence, The torque is $2\sqrt{2q}\ N-m$

Learn more :

Topic : Torque

https://brainly.in/question/7709241