Two uniformly long charged wires with linear densities λ and 3λ are placed along X and Y axis respectively. Determined the slope of electric field at any point on the line y=√3 x .

Question

Two uniformly long charged wires with linear densities λ and 3λ are placed along X and Y axis respectively. Determined the slope of electric field at any point on the line y=√3 x . (A) 3√3 (B) (√3/3 √2) (C) (1/3 √3) (D) √3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-8k67xo5b4jho.png" /> Ex=(3 λ /2 π Ïµo x) Ey=(λ /2 π Ïµo x √3) overset arrow E=(3 λ /2 π Îµ0 x) hati+(λ /2 π Îµ0 x √3) hatj textSlope=(E texty/E textx)=( text1/√ text3)× (/3)=( text1/ text3 √ text3)

Q. Two uniformly long charged wires with linear densities $λ$ and $3 λ$ are placed along $X$ and $Y$ axis respectively. Determined the slope of electric field at any point on the line $y = 3 x$ .

$33$

$\frac{3}{3 2}$

$\frac{1}{3 3}$

$3$

$E_{x} = \frac{3 λ}{2 π ϵ _{o} x}$
$E_{y} = \frac{λ}{2 π ϵ _{o} x 3}$
$E \to = \frac{3 λ}{2 π ε _{0} x} \hat{i} + \frac{λ}{2 π ε _{0} x 3} \hat{j}$
$Slope = \frac{E _{y}}{E _{x}} = \frac{1}{3} \times 3 = \frac{1}{3 3}$

Q. Two uniformly long charged wires with linear densities λ and 3λ are placed along X and Y axis respectively. Determined the slope of electric field at any point on the line y=3​x .

33​

32​3​​

33​1​

3​

Ex​=2πϵo​x3λ​ Ey​=2πϵo​x3​λ​ E→=2πε0​x3λ​i^+2πε0​x3​λ​j^​ Slope=Ex​Ey​​=3​1​×3​=33​1​

Q. Two uniformly long charged wires with linear densities $λ$ and $3 λ$ are placed along $X$ and $Y$ axis respectively. Determined the slope of electric field at any point on the line $y = 3 x$ .

$33$

$\frac{3}{3 2}$

$\frac{1}{3 3}$

$3$

$E_{x} = \frac{3 λ}{2 π ϵ _{o} x}$
$E_{y} = \frac{λ}{2 π ϵ _{o} x 3}$
$E \to = \frac{3 λ}{2 π ε _{0} x} \hat{i} + \frac{λ}{2 π ε _{0} x 3} \hat{j}$
$Slope = \frac{E _{y}}{E _{x}} = \frac{1}{3} \times 3 = \frac{1}{3 3}$