The electric potential V in volts in a region of space is given by V=a x2+a y2+2 a z2 . The work done by field when a 2 μ C test charge moves from point (0,0,0.1) m to origin is 5 × 10-5 J. Determine a.

Question

The electric potential V in volts in a region of space is given by V=a x2+a y2+2 a z2 . The work done by field when a 2 μ C test charge moves from point (0,0,0.1) m to origin is 5 × 10-5 J. Determine a. (A) 1000 (B) 650 (C) 1500 (D) 1250

Tardigrade Admin · Accepted Answer

V1 =a(0)2+a(0)2+2 a(0.1)2 =(a/50) V0 =0 arrow at origin. We l =q(V1-V0) ⇒ 5 × 10-5=2 × 10-6[(a/50)-0] ⇒ a =1250

Q. The electric potential $V$ in volts in a region of space is given by $V = a x^{2} + a y^{2} + 2 a z^{2} .$ The work done by field when a $2 μ C$ test charge moves from point $(0, 0, 0.1) m$ to origin is $5 \times 1 0^{- 5} J$ . Determine $a$ .

1000

650

1500

1250

$V_{1} = a (0)^{2} + a (0)^{2} + 2 a (0.1)^{2}$
$= \frac{a}{50}$
$V_{0} = 0 \to$ at origin.
$W_{e l} = q (V_{1} - V_{0})$
$\Rightarrow 5 \times 1 0^{- 5} = 2 \times 1 0^{- 6} [\frac{a}{50} - 0]$
$\Rightarrow a = 1250$

Q. The electric potential V in volts in a region of space is given by V=ax2+ay2+2az2. The work done by field when a 2μC test charge moves from point (0,0,0.1)m to origin is 5×10−5J. Determine a.

1000

650

1500

1250

V1​=a(0)2+a(0)2+2a(0.1)2 =50a​ V0​=0→ at origin. Wel​=q(V1​−V0​) ⇒5×10−5=2×10−6[50a​−0] ⇒a=1250

Q. The electric potential $V$ in volts in a region of space is given by $V = a x^{2} + a y^{2} + 2 a z^{2} .$ The work done by field when a $2 μ C$ test charge moves from point $(0, 0, 0.1) m$ to origin is $5 \times 1 0^{- 5} J$ . Determine $a$ .

$V_{1} = a (0)^{2} + a (0)^{2} + 2 a (0.1)^{2}$
$= \frac{a}{50}$
$V_{0} = 0 \to$ at origin.
$W_{e l} = q (V_{1} - V_{0})$
$\Rightarrow 5 \times 1 0^{- 5} = 2 \times 1 0^{- 6} [\frac{a}{50} - 0]$
$\Rightarrow a = 1250$