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Variation of Specific, Equivalent and Molar Conductivities with Concentration

An electric f...

Question

An electric field is expressed as $\to E = 2^i + 3^j$ . Find the potential difference $(V_{A} - V_{B})$ between two points $A$ and $B$ whose position vectors are given by ${\to r}_{A} =^i + 2^j$ and ${\to r}_{B} = 2^i +^j + 3^k$ :

A

- 1 V

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B

1 V

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C

2 V

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D

3 V

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Solution

The correct option is A $- 1 V$
$d V = - \to E . \to d x - \to E . \to d y$
$Δ V = - \int E d x - \int E d y$
$V_{B} - V_{A} = - (\int_{1}^{2} 2 d x + \int_{2}^{1} 3 d y)$
$= - [2 (2 - 1) + 3 (1 - 2)]$
$= - [2 - 3] = 1 V$
Hence, $V_{A} - V_{B} = - 1 V$

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Similar questions

Q. An electric field is expressed as

\to E = 2^i + 3^j

. Find the potential difference

(V_{A} - V_{B})

between two points A and B whose position vectors are given by

r_{A} =^i + 2^j

r_{B} = 2^i +^j + 3^k .

Q. Find potential difference

V_{A B}

between two points

A

B

whose position vectors are

r_{A} = (^i - 2^j +^k) m

r_{B} = (2^i +^j - 2^k) m

, in an uniform electric field

E = (2^i + 3^j + 4^k) N/C

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Q. An electric field

\to E = (2^i + 3^j) N / C

exists in space. The potential difference

(V_{P} - V_{Q})

between two points

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Q

whose position vectors

_{P} =^i + 2^j

_{Q} = 2^i +^j +^k

Q. Calculate the potential difference between points

A

B

in an electric field

\to E = (2^i + 3^j + 4^k) {NC}^{- 1}

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B

{\to r}_{A} = (^i - 2^j +^k) m

{\to r}_{B} = (2^i +^j - 2^k) m

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2^i +^j -^k

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