R and S are two points in the electric field of a small negatively charged sphere Q. Two charges of Q1=+3nC and Q2=-4nC are separated by a distance of 40cm. What is the electric field strength at a ?

To find the electric field strength at point A due to the small negatively charged sphere Q, we need to consider the electric fields created by the two charges Q1 and Q2 separately.

The electric field strength at point A due to a point charge Q is given by the formula:

E = k * |Q| / r^2

Where:
E = electric field strength
k = Coulomb's constant (8.99 x 10^9 N m^2/C^2)
|Q| = magnitude of the charge
r = distance between the charge and the point where the electric field is being measured

For charge Q1 (+3nC):
E1 = k * |Q1| / r^2
E1 = (8.99 x 10^9) * (3 x 10^-9) / (0.4)^2
E1 = 67.425 N/C

For charge Q2 (-4nC):
E2 = k * |Q2| / r^2
E2 = (8.99 x 10^9) * (4 x 10^-9) / (0.4)^2
E2 = 89.9 N/C

Since the electric field is a vector quantity, we need to consider the direction of the electric fields due to Q1 and Q2. The electric field due to Q1 will be directed away from Q1 (positive charge) and the electric field due to Q2 will be directed towards Q2 (negative charge).

Therefore, the net electric field at point A will be the vector sum of the electric fields due to Q1 and Q2:

E_net = E1 - E2
E_net = 67.425 - 89.9
E_net = -22.475 N/C

So, the electric field strength at point A due to the small negatively charged sphere Q is 22.475 N/C directed towards the point.

Step 1: Calculate the net electric field at point P due to both charges.

The electric field due to Q1 is given by:

```
E1 = k - Q1 / d^2
```

where:

- E1 is the electric field due to Q1
- k is Coulomb's constant (9 - 10^9 N m^2 C^-2)
- Q1 is the charge of Q1 (3 nC)
- d is the distance between Q1 and P (20 cm or 0.2 m)

```
E1 = (9 - 10^9 N m^2 C^-2) - (3 - 10^-9 C) / (0.2 m)^2
E1 = 675 N/C
```

The electric field due to Q2 is given by:

```
E2 = k - Q2 / d^2
```

where:

- E2 is the electric field due to Q2
- k is Coulomb's constant (9 - 10^9 N m^2 C^-2)
- Q2 is the charge of Q2 (-4 nC)
- d is the distance between Q2 and P (20 cm or 0.2 m)

```
E2 = (9 - 10^9 N m^2 C^-2) - (-4 - 10^-9 C) / (0.2 m)^2
E2 = -360 N/C
```

The net electric field at P is the vector sum of E1 and E2:

```
E_net = E1 + E2
E_net = 675 N/C - 360 N/C
E_net = 315 N/C
```

Step 2: The electric field strength at point P is 315 N/C.