A straight rod of length 20cm is charged uniformly by -40nC charge.Find the electric intensity at a point lying on the axis of the rod at a distance 50cm from its midpoint?

Question

Answer

Calculating Electric Intensity of a Charged Rod

Given:

Length of the rod = 20cm

Charge of the rod = -40nC

Distance of the point from the midpoint of the rod = 50cm

Calculating Electric Intensity:

Electric intensity is the force experienced per unit charge.

Using the formula for electric intensity for a point charge:

E = kq/r^2

where E = electric intensity, k = Coulomb's constant = 9x10^9 Nm^2/C^2, q = charge of the rod, and r = distance of the point from the midpoint of the rod

Dividing the rod into small segments of length dx:

dE = kQdx/(x^2 + r^2)^3/2

where Q = charge of the segment at a distance x from the midpoint of the rod

Integrating dE from -L/2 to L/2:

E = kQ/L * [1/(r-d/2) - 1/(r+d/2)]

where L = length of the rod, d = distance of the point from the midpoint of the rod, and Q = charge of the entire rod

Substituting the given values:

L = 20cm = 0.2m

d = 50cm = 0.5m

Q = -40nC = -4x10^-8 C

Calculating the electric intensity:

E = 9x10^9 * (-4x10^-8) / 0.2 * [1/(0.5-0.1) - 1/(0.5+0.1)] = -5.4x10^4 N/C

Conclusion:

The electric intensity at a point lying on the axis of the rod at a distance 50cm from its midpoint is -5.4x10^4 N/C.

Answer

E=2klemda /R where k is 9×10^9 and lemda is charge per unit length and R is the distance 50cm then lemda is 40×10^-9/0.2 then lemda is 200 ×10^-9 and then E =2×9×10^9×200×10^-9/0.5  then after solving it 7200 ans

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