Question

20.
Charge is distributed along the x-axis from x=0
to x=L = 50.0 cm in such a way that its linear
charge density is given by a = ax?, where a =
18.0 °C m?. Calculate the total charge in the
region 0<x<L.
Sol:​

Answer 1

Explanation:

Electric field dE=

r

2

Kdq

now we know that 80μC charge is uniformly distributed between x=0 and x=2

Charge on per unit length=

2

80

=40μC

now electric field due to some charge dq is dE=

(8−x)

2

Kdq

E=∫

0

2

(8−x)

2

Kdq

E=∫

0

2

(8−x)

2

K(40)dx

=K(40)(

6

1

−

8

1

)=15X10

9

N/C

Answer 2

Linear charge density, λ=q/L=ax²

⇒ q/L=ax²

q=Lax²=ax³

q=(18mC/m³)(1/2m)³

q=2.25 mC=2.25×10^(-3) C