Question

A line of positive charge is formed into a semicircle of radius R 80.0 cm, as shown in the figure below. The charge per unit length along the semicircle is given by the expression λ-, cos@). The total charge on the semicircle is 13.0 μC. Calculate the total force on a charge of 2.00 μC placed at the center of curvature magnitude direction Select

Answer 1

The total charge on the semi circle is given to be  .

That is  

For one quadrant (ie from y axis to x axis), since the charge distribution is dependent on theta, we can find the charge in one half of this semi cirlce and then multiply it with 2 to get the total charge.

so

Now, the x component of the force experienced by the by the component of the semi circle to the left of y axis and to the right of y axis will be the same, but in opposite direction. Therefore, they will cancel out each other. So only the y component of the force will remain( this is because but , thus cancels each other out).

The y component force is given by the equation

here we substituted the value for dl as we took earlier.

solving, we get

$F_{y}=0.8281N$