Question

Figure shows a non-conducting semi-circular rod in $x-y$ plane. Top half (quarter circle) has uniform linear charge density $-\lambda$ whereas remaining half has uniform linear charge density $+\lambda$. What is the direction of the net electric field at point $P$?

• A. Along $+y$ axis
• B. Electric field is zero at point $P$, so direction cannot be determined
• C. Along the bisector of x-axis and y-axis
• D. Along $+x$ axis

Answer 1

Answer: (A)

Along $+y$ axis

Consider any two symmetric dipole elements, net contribution due to these elements at point $P$ is along $+y-axis$. Similarly, by principle of superposition, we can say that net electric field at point $P$ directed along $+y-axis$.