The dipole moment of the given charge distribution is:

Question

The dipole moment of the given charge distribution is: (A) -(4Rq/π ) hati (B)  (4Rq/π ) hati (C) -(2Rq/π ) hati (D) (2Rq/π ) hati

Tardigrade Admin · Accepted Answer

P Q =2 R cos θ d p =d q × 2 R cos θ d r =λ(R d θ) × 2 R cos θ p =2 λ R2 ∫ limits0T / 2 cos d θ =2 λ R2| sin θ|π/20 p =2 λ R2 vecp =2 (2 q/π R) × l2=(4 q R/π) i

Q. The dipole moment of the given charge distribution is:

$- \frac{4 R _{q}}{π} \hat{i}$

$\frac{4 R _{q}}{π} \hat{i}$

$- \frac{2 R _{q}}{π} \hat{i}$

$\frac{2 R _{q}}{π} \hat{i}$

$PQ = 2 R cos θ$
$d p = d q \times 2 R cos θ$
$d r = λ (R d θ) \times 2 R cos θ$
$p = 2 λ R^{2} 0 \int T /2 cos d θ$
$= 2 λ R^{2} ∣ sin θ ∣_{0}^{π /2}$
$p = 2 λ R^{2}$
$p = 2 \frac{2 q}{π R} \times l^{2} = \frac{4 qR}{π} i$

Q. The dipole moment of the given charge distribution is:

−π4Rq​​i^

π4Rq​​i^

−π2Rq​​i^

π2Rq​​i^

PQ=2Rcosθ dp=dq×2Rcosθ dr=λ(Rdθ)×2Rcosθ p=2λR20∫T/2​cosdθ =2λR2∣sinθ∣0π/2​ p=2λR2 p​=2πR2q​×l2=π4qR​i

$- \frac{4 R _{q}}{π} \hat{i}$

$\frac{4 R _{q}}{π} \hat{i}$

$- \frac{2 R _{q}}{π} \hat{i}$

$\frac{2 R _{q}}{π} \hat{i}$

$PQ = 2 R cos θ$
$d p = d q \times 2 R cos θ$
$d r = λ (R d θ) \times 2 R cos θ$
$p = 2 λ R^{2} 0 \int T /2 cos d θ$
$= 2 λ R^{2} ∣ sin θ ∣_{0}^{π /2}$
$p = 2 λ R^{2}$
$p = 2 \frac{2 q}{π R} \times l^{2} = \frac{4 qR}{π} i$