QJEEM16Ph8d39: JEE Main 2016 Physics - Class 12 JEEM16Ph8d39 Solution: The potential (in volts) of a charge distribution is given by.…

Question

Verified Solution • 2025–26 Session moderate

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

V(z) = 30

-

5x² for

| z |

\leq

1 m.
V(z) = 35

-

10

| z |

for

| z |

\geq

1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume

ρ_{0}

(in units of

ε_{0}

) which is spread over a certain region, then choose the correct statement.

Accepted Answer

We know,

E(z) =

-

\frac{d v}{d z}

∴

E(z) =

-

10 z for

| z | \leq 1

m

and E(z) = 10 for

| z | \geq 1

m

∴

The source is an infinity large non conducting thick of thickness z = 2 m.

∴

E =

\frac{σ}{2 ε_{0}}

=

\frac{ρ (2)}{2 ε_{0}}

=

\frac{ρ}{ε_{0}}

∴

\frac{ρ}{ε_{0}}

= 10

\Rightarrow

ρ

=

10 ε_{0}

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