Four positive point charges +q are kept at the four corners of a square of side l. The net electric field at the mid-point of any one side of the square is (. Take, .(1/4 π ε0)=k)

Question

Four positive point charges +q are kept at the four corners of a square of side l. The net electric field at the mid-point of any one side of the square is (. Take, .(1/4 π ε0)=k) (A) (4kq/l2)  (B) (16 kq/5 √5 l2) (C) (8kq/5 √5 l2) (D) (kq/ l2)

Tardigrade Admin · Accepted Answer

The force at midpoint of any side of a square let's say at point

P

which is midpoint of side

A B

is due to charges at corners

A, B, C

and

D

F_{P} = F_{A P} + F_{BP} + F_{CP} + F_{D P}

A P = D P = l

BP = CP = l^{2} + (l /2)^{2} = 5 l^{2} /4

Electric field due to charges at

A

and

D

will be equal in magnitude and opposite in direction, so will cancel each other.
Similarly, the vertical components of electric field due to charges at

B

and

C

will also cancel each other, but the horizontal components of these will add up to give resultant electric field.

E = 2 \cdot \frac{k q}{( 5 l ^{2} /4 ) ^{2}} \cdot cos θ

= 2 \times \frac{4 k q}{5 l ^{2}} \times \frac{2}{5} = \frac{16 k q}{5 5 l ^{2}}

Q. Four positive point charges $+ q$ are kept at the four corners of a square of side $l$ . The net electric field at the mid-point of any one side of the square is $($ Take, $\frac{1}{4 π ε _{0}} = k)$

$\frac{4 k q}{l ^{2}}$

$\frac{16 k q}{5 5 l ^{2}}$

$\frac{8 k q}{5 5 l ^{2}}$

$\frac{k q}{l ^{2}}$

Q. Four positive point charges +q are kept at the four corners of a square of side l. The net electric field at the mid-point of any one side of the square is ( Take, 4πε0​1​=k)

l24kq​

55​l216kq​

55​l28kq​

l2kq​

Q. Four positive point charges $+ q$ are kept at the four corners of a square of side $l$ . The net electric field at the mid-point of any one side of the square is $($ Take, $\frac{1}{4 π ε _{0}} = k)$

$\frac{4 k q}{l ^{2}}$

$\frac{16 k q}{5 5 l ^{2}}$

$\frac{8 k q}{5 5 l ^{2}}$

$\frac{k q}{l ^{2}}$