The radial electric field E ⃗ = a r 2 e − r k r ^ \vec{E}=\frac{a}{r^2}e^{-\frac{r}{k}}\hat{r} E = r 2 a e − k r r ^ is produced by a point charge q₀=4πε₀a at the origin plus a continuous surrounding charge distribution.The total continuous charge q spread around the origin is:

Question

The radial electric field E ⃗ = a r 2 e − r k r ^ \vec{E}=\frac{a}{r^2}e^{-\frac{r}{k}}\hat{r} E = r 2 a ​ e − k r ​ r ^ is produced by a point charge q₀=4πε₀a at the origin plus a continuous surrounding charge distribution.The total continuous charge q spread around the origin is:

G1 Physics · Accepted Answer

The total enclosed charge at radius r is Q e n c ( r ) Q_enc(r) Q e ​ n c ( r ) = 4πε₀a e ( − r / k ) . e^(-r/k). e ( − r / k ) . As r→∞, Q t o t a l Q_total Q t ​ o t a l = 0. Thus the surrounding continuous charge is q = Q t o t a l Q_total Q t ​ o t a l - q₀ = -4πε₀a.

The radial electric field E ⃗ = a r 2 e − r k r ^ \vec{E}=\frac{a}{r^2}e^{-\frac{r}{k}}\hat{r} E = r 2 a ​ e − k r ​ r ^ is produced by a point charge q₀=4πε₀a at the origin plus a continuous surrounding charge distribution.The total continuous charge q spread around the origin is:

The radial electric field E ⃗ = a r 2 e − r k r ^ \vec{E}=\frac{a}{r^2}e^{-\frac{r}{k}}\hat{r} E = r 2 a e − k r r ^ is produced by a point charge q₀=4πε₀a at the origin plus a continuous surrounding charge distribution.The total continuous charge q spread around the origin is: