Electric Potential Due to a Solid Sphere of Charge

Q. Two uniformly charged infinite wires each having charge density λ are placed along x and y axis as shown in the figure. The magnitude of electric field intensity at point P will be

समान आवेश घनत्व λ वाले दो एकसमान रूप से आवेशित अनन्त तारों को चित्रानुसार x व y-अक्ष के अनुदिश रखा गया है। बिंदु P पर विद्यतुक्षेत्र तीव्रता का परिमाण होगा

1. $\frac{\lambda }{\pi {\epsilon }_{0}d}$
2. $\frac{2\lambda }{\pi {\epsilon }_{0}d}$
3. $\frac{\lambda }{\sqrt{2}\pi {\epsilon }_{0}d}$
4. Zero
   
   शून्य

Q. Two metal spheres are very far apart but are connected by a thin wire as shown-


If the combined charge of both the sphere is $Q$, then the common potential will be

1. $\frac{-kQ}{r_1{r}_2}$
   
2. $\frac{kQ}{r_1+r_2}$
   
3. $\frac{kQ}{r_1-r_2}$
   
4. $\frac{-kQ}{r_1+r_2}$
   

Q. A large hollow metallic sphere $A$ (of radius $R$ ) is positively charged to a potential of $100\text{V}$ and a small sphere $B$ (of radius $\frac{R}{5}$) is also positively charged to a potential of $100\text{V}$. Now $B$ is placed inside $A$ and they are connected by a wire. The final potential of $A$ will be:

1. $200\text{V}$
2. $150\text{V}$
3. $120\text{V}$
4. none of above

Q. A charge $+Q$ is uniformly distributed over a thin ring of radius $R$. Find the velocity of a negative point charge $-Q$ at the moment it passes through the centre of the ring if it has mass $m$ and was initially at rest at infinity on the axis of the ring.

1. $Q\sqrt{\frac{2k}{mR}}$
2. $0$
3. $2Q\sqrt{\frac{k}{mR}}$
4. $\sqrt{\frac{2kQ}{mR}}$