Question

Four charges +Q, +2Q, +3Q and +4Q are placed at the corners of a square ABCD of side 0.1m respectively. The electric field at the centre of the square is 5.1x103N/C. Find the value of Q

Answer 1

Answer:

7.08×10^-10 Coulomb

Explanation:

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Answer 2

The value of Q is 0.7nC.

Given:-

Charges = q1 = +Q

q2 = +2Q

q3 = +3Q

q4 = +4Q

Side of square= 0.1m

Electric field at centre = 5.1* 10³N/C

To Find:-

The value of Q.

Solution:-

We can find out the the value of Q by using the following methods.

Now,

Charges = q1 = +Q

q2 = +2Q

q3 = +3Q

q4 = +4Q

Side of square= 0.1m

Electric field at centre = 5.1* 10³N/C

According to the formula,

E/F due to q1,

$e1 = \frac{kq}{ {r}^{2} }$

r = d/√2

$e1 = \frac{2kq}{ {d}^{2} }$

Similarly, E/F due to q2, q3 and q4 are respectively,

$e2 = \frac{4kq}{ {d}^{2} }$

$e3 = \frac{6kq}{ {d}^{2} }$

$e4 = \frac{8kq}{ {d}^{2} }$

on solving, we get

$e = \frac{8kq}{ {d}^{2} }$

$q = \frac{e {d}^{2} }{8k}$

$q = \frac{5.1 \times {10}^{3} \times {0.1}^{2} }{8 \times 9 \times {10}^{9} }$

$q = \frac{5.1 \times {10}^{ - 8} }{72}$

$q = 7 \times {10}^{ - 10}$

$q = 0.7 \times {10}^{ - 9}$

q = 0.7nC

Hence, The value of Q is 0.7nC.

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