Question

A uniformly charged rod of length 4 cm and linear charge density 30 micro C/m is placed as shown in figure. Calculate the x-component of electric field at point p. A uniformly charged rod of length 4 cm and linear charge density 30 micro C/m is placed as shown in figure.

Answer 1

see free body diagram,

Let us consider an elementary length dx

so, charge on element , dQ = $\lambda dx$

where $\lambda$ is linear charge density of rod.

x - component of electric field at point P, Ex = dEsinA

= kdQ/(x² + r²) × x/√(x² + r²)

= $\frac{k\lambda dx}{(x^2+r^2)^{3/2}}$

from diagram, tanA = x/r

or, x = rtanA

differentiating both sides,

dx = rsec²A dA

so, Ex = $\frac{k\lambda xdx}{(rtan^2A+r^2)^{3/2}}$

= $\frac{k\lambda r^2tanA. sec^2A dA}{sec^3A}$

= $\frac{k\lambda}{r}\int\limits^{\theta}_0{sinA}\,dA$

= $\frac{k\lambda}{r} (1-cos\theta)$

here, $cos\theta=\frac{3}{\sqrt{4^2+3^2}}=\frac{3}{5}$

so, Ex = $\frac{2k\lambda}{5r}$

now putting, k and linear charge density

Ex = 2 × 9 × 10^9 × 30 × 10^-6/5 × 3cm

= 36 × 10^5 N/C

hence, answer is 36 × 10^5 N/C

Answer 2

Answer:

Answer is 36×10^5 V/m

Must remember a formula -

Ex - K(lamda) (costheta2-costheta1) /r

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