The electric potential V (in volt) varies with x (in metre) according to the relation V=(5+4 x2) The force experienced by a negative charge of 2 × 10-6 C located at x=0.5 m is

Question

The electric potential V (in volt) varies with x (in metre) according to the relation V=(5+4 x2) The force experienced by a negative charge of 2 × 10-6 C located at x=0.5 m is (A) 2 × 10-6 N (B) 4 × 10-6 N (C) 6 × 10-6 N (D) 8 × 10-6 N

Tardigrade Admin · Accepted Answer

Given, V =5+4 x2 (d V/d r)=E ∴ (d V/d x)=8 x=E or E=8 × 0.5=4 Vm -1 Now, F =q E =2 × 10-6 × 4 =8 × 10-6 N

Q. The electric potential $V$ (in volt) varies with $x$ (in metre) according to the relation $V = (5 + 4 x^{2})$ The force experienced by a negative charge of $2 \times 1 0^{- 6} C$ located at $x = 0.5 m$ is

$2 \times 1 0^{- 6} N$

$4 \times 1 0^{- 6} N$

$6 \times 1 0^{- 6} N$

$8 \times 1 0^{- 6} N$

Given, $V = 5 + 4 x^{2}$
$\frac{d V}{d r} = E$
$∴ \frac{d V}{d x} = 8 x = E$
or $E = 8 \times 0.5 = 4 V m^{- 1}$
Now, $F = qE$
$= 2 \times 1 0^{- 6} \times 4$
$= 8 \times 1 0^{- 6} N$

Q. The electric potential V (in volt) varies with x (in metre) according to the relation V=(5+4x2) The force experienced by a negative charge of 2×10−6C located at x=0.5m is

2×10−6N

4×10−6N

6×10−6N

8×10−6N