JEE Main 2016 · 9 Apr · Shift 1 · Physics Q12

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PhysicsSingle correct+4 / -1Question 12 of 90

The potential (in volts) of a charge distribution is given by

$V(z)=30-5z^2$ for |z| ≤ 1 m

V(z) = 35 − 10 |z| for |z| ≥ 1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $\rho_0$ (in units of $\epsilon_0$ ) which is spread over a certain region, then choose the correct statement.

\rho_0=10\,\epsilon_0

for |z| ≤ 1 m and

\rho_0=0

elsewhere

\rho_0=20\,\epsilon_0

in the entire region

\rho_0=40\,\epsilon_0

in the entire region

\rho_0=20\,\epsilon_0

for |z| ≤ 1 m and

\rho_0=0

elsewhere

Answer and worked solution

Official answer: A

From Gauss's law in one dimension, $\rho=-\epsilon_0\frac{d^2V}{dz^2}$ . For $|z|\le1$ , $V''=-10$ , so $\rho_0=10\epsilon_0$ ; outside, V is linear and $\rho=0$ .

Topics:Electric flux and Gauss's law Electric potential

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JEE Main 2016 · 9 Apr · Shift 1, Physics question 12