Due to a point charge potential and field at a point A are 7 and 3 res...
Understanding the Problem
We have two points, A and B, influenced by a point charge. The potential and electric field at point A are given as follows:
- Potential at A (VA) = 7 V
- Electric Field at A (EA) = 3 N/C
At point B, the potential is less than the potential at A, and the electric field is initially less than 3 N/C. When the charge is tripled, the electric field at B becomes 3 N/C.
Key Concepts
- The potential (V) due to a point charge is given by V = k * Q / r, where k is the Coulomb's constant, Q is the charge, and r is the distance from the charge.
- The electric field (E) is given by E = k * Q / r^2.
Initial Conditions at Point B
1. Since the electric field at B is initially less than 3 N/C, let’s denote it as E_B < 3="" />
2. The potential at B (VB) is less than VA, so VB < 7="" />
Effect of Tripling the Charge
When the charge is tripled, the new electric field at point B becomes:
- New Electric Field at B (E'_B) = 3 N/C.
Using the relationship of electric field, we can write:
E'_B = k * (3Q) / r^2 = 3 N/C.
This implies that the distance (r) from the point charge to point B has not changed.
Calculating the New Potential at Point B
The new potential at point B after tripling the charge can be calculated as:
V'_B = k * (3Q) / r.
Since we know the original potential at point B was less than 7 V, we can consider the change:
- Original Potential (VB) < 7="" />
- New Potential (V'_B) = 3 * Original Potential (VB) (due to tripling the charge)
Thus, we can infer:
V'_B = 3 * (VB) < 3="" *="" 7="21" />
Since the new electric field at B is now 3 N/C, it confirms that the potential at B must have increased significantly, leading to:
Final Answer
The potential at point B now is 21 V.
Due to a point charge potential and field at a point A are 7 and 3 res...
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