Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
A cone is made of insulating material that has a total charge Q spread uniformly spread over its sloping surface. Calculate the work done in bringing a small test charge q from infinity to the apex of the cone. The cone has a slope length L.

```
6 years ago IIT Delhi
174 Points
```							Put the apex of the cone at the origin. Let it have a base radius R parallel to the y axis, and a height, h along the x axis. This means L = (R^2 + h^2)^(1/2).We need an area element. Since we can use rotational symmetry about the apex, I will consider the area of a slice of the cone normal to the x axis. This area is 2py(ds) where ds is the infinitesimal arc length of the slice. I will argue that:dA = 2p(R/h)x(1 + (R/h)^2)^(1/2)dxIf you integrate dA from x=0..h, you obtain pRL, the surface area of a cone, so that works fine.Now we know that dV = ksdA/r = ks2p(R/h)x(1 + (R/h)^2)^(1/2)/((1 + (R/h)^2)^(1/2)x)dx= ks2p(R/h)dx, where s represents the surface charge density.Integrating dV from 0 . . h is simply ks2pR, and since s = Q/(pRL) this means V of the apex = 2kQ/L. The work needed to bring in charge q from infinity is qV = 2kQq/L.Sher MohammadFaculty askiitians
```
6 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Electrostatics

View all Questions »  ### Course Features

• 101 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions