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

Question

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

Tardigrade Admin · Accepted Answer

overset arrow E=(3 λ /2 π ∈ 0 x) hati+(λ /2 π ∈ 0 x √3) hatj <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-kajq9067iqc8.png" /> Slope= (Ey/Ex)=(1/√3)÷3=(1/3 √3)

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

$33$

$\frac{3}{3 2}$

$\frac{1}{3 3}$

$3$

$E \to = \frac{3 λ}{2 π \in _{0} x} \hat{i} + \frac{λ}{2 π \in _{0} x 3} \hat{j}$

$Sl o p e = \frac{E _{y}}{E _{x}} = \frac{1}{3} \div 3 = \frac{1}{3 3}$

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

33​

32​3​​

33​1​

3​

E→=2π∈0​x3λ​i^+2π∈0​x3​λ​j^​ Slope=Ex​Ey​​=3​1​÷3=33​1​

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

$33$

$\frac{3}{3 2}$

$\frac{1}{3 3}$

$3$

$E \to = \frac{3 λ}{2 π \in _{0} x} \hat{i} + \frac{λ}{2 π \in _{0} x 3} \hat{j}$

$Sl o p e = \frac{E _{y}}{E _{x}} = \frac{1}{3} \div 3 = \frac{1}{3 3}$